







A limit 
20170514 

From Soham: Find out the value of the following:
lim (x+x^2 +x^3 +.........x^n–n)/(x–1)
x→1 Answered by Penny Nom. 





A tolerance limit is 0.5% 
20170106 

From Joe: Dear Sir/Madam,
How can I describe the following.
My volume tolerance limit is 0.5%,regardless of quantity.
Say , My total volume output is 344,714 Litres and benchmark volume is 348,194
Difference of 3480Litres, this would give me a percentage of 0.999.
Which is above my tolerance.
How can I explain this high tolerance limit even though volume difference is minimal.
Regards
Joe Answered by Penny Nom. 





A limit of a rational function 
20160116 

From selvamani: F (x) = x^3+3x^29x2 / x^3x6 and limit x tends to 2, f (x) exist then limit x tends to 2, f (x) is equal to ? How to answer this problem. Answered by Penny Nom. 





A limit 
20150313 

From arthur: sin(x1)/x^+x2 Answered by Penny Nom. 





A limit 
20150219 

From genc: Lim (27x^31) / (3x1)
X> 1/3 Answered by Harley Weston. 





A limit with trig functions 
20140222 

From pearl: (what is the value of limit of x as it approaches 0 of sin8x divided by cos6x) Answered by Penny Nom. 





Is a line lying in a plane an open or a closed region? 
20130213 

From pardeep: please help with this question on the open and closed intervals ::
Is a line lying in a plane an open or a closed region? my teacher says it is a closed region reasoning out that it contains all it boundary points. please help how is it so? Answered by Harley Weston. 





1+2+4+8....= 1 
20120402 

From Andy: In this minutephysics video, it's claimed that 1+2+4+8....= 1
Is this true, and if so, how?
< href="http://www.youtube.com/watch?v=kIq5CZlg8Rg">http://www.youtube.com/watch?v=kIq5CZlg8Rg Answered by Robert Dawson. 





A limit 
20120118 

From Neil: The limit of [(1/x)^3  1/8]^1/3 all over (x  1/2) as x approaches 1/2 to positive infinity. How to answer that? Answered by Harley Weston. 





Limits and composition 
20111230 

From Rahul: I want to know about limit proofs of composite functions. Like limit of log of a function equals log of limit of the function Answered by Penny Nom. 





The derivative of f(x) = (x+1)^1/2 
20110905 

From Carla: Find the derivative using the limit process of
f(x) = (x+1)^1/2 Answered by Harley Weston. 





limit as x approaches a of ((x^(1/2))(a^(1/2)))/(xa)? 
20100929 

From emily: limit as x approaches a of ((x^(1/2))(a^(1/2)))/(xa)? Answered by Penny Nom. 





A limit 
20100927 

From norma: I have a problem like this one but I can get it right. please help me to answer
find the constant a such that the function is continuous on the entire line.
g(x)= {x^2  a^2 / xa if x is not = a
{6 if x = a Answered by Penny Nom. 





Limits 
20100920 

From rodrigo: what's the limit of x+1/x1, when x tends to 1? Answered by Janice Cotcher. 





Using the limit definition 
20100606 

From Meagan: Using the limit definition find the derivative of 3/(2x^2) Answered by Harley Weston. 





The derivative using limits 
20090421 

From Kirstin: I am trying to take the limit of f(x) = [f(x+h)f(x)] / h
If you try taking the limit by substituting the limiting value h=0, you get 0/0,
which of course is not the right answer. You rewrite f(x+h)f(x) so it has a factor
of h in it, which you cancel with the h in the denominator before you substitute h=0.
But I am not sure how to do this. Thanks. Answered by Robert Dawson. 





Infinite sets and infinite limits 
20090306 

From Justin: Hello, I know I have asked a similar question before but I was just wondering if set theory applies to the lim x>0, y=1/x=infinity and if so, what type of infinity would it be? Thanks a lot for your help with this question!
Regards,
Justin Answered by Robert Dawson and Harley Weston. 





A trig limit 
20090205 

From Samantha: lim x> 0 ( ( r*cos(wt +h) + r*cos(wt) )/ h )
Where r & w are constants. Answered by Harley Weston. 





A trig limit 
20090205 

From Kathy: Hi! I was just wondering how to do this question:
lim 1cos2x/xsinx as x approaches 0
Thanks,
Kathy Answered by Penny Nom. 





limit sinx/x 
20090130 

From Jackie: how to evaluate limit sinx/x as x tends to zero if x is in degrees Answered by Stephen La Rocque and Harley Weston. 





Limit of a Trig Function 
20081206 

From Berta: Evaluate limit xcsc2x/cos 5x as x goes to 0
ans is 2 but I get 1/2
x/sin2xcos5x = 2x/2sin2xcos5x= 1/2cos5x Answered by Penny Nom. 





A trig limit 
20081104 

From Teri: Although I have this problem completely worked out in front of me I still cannot understand
how it was done. The problem is:
Find the limit.
lim x>0 sin2x/tan7x. Answered by Harley Weston. 





Limit as it Approaches a Constant 
20080916 

From Brooks: what is the limit as x approaches 10 for f(x) = sqrt(x1) = 3 pleeeeeaase help me out here Answered by Janice Cotcher. 





Right Sided Limit of an Exponential Function 
20080729 

From joseph: I am trying to find the limit as X approaches 0 from the positive side of x to the sin of x
which look like this lim x^sinx
x>0+ Answered by Harley Weston. 





Limit as it Approaches Infinity 
20080729 

From mary: i was trying to find the limit of this problem
the limit as x approches infinity of x minus cosx divided by x
lim xcosx/x
x>oo Answered by Harley Weston. 





limit x>0 (logxlog(x1)) 
20080522 

From kritica: lt x>0 (logxlog(x1)) Answered by Harley Weston. 





lim as x approaches infinite of 5x + 2/x1 
20080404 

From Jordan: how to solve this.
lim as x approaches infinite of 5x + 2/x1 Answered by Stephen La Rocque and Harley Weston. 





The limit of (sin4x)/(tan9x) as x approaches zero 
20080314 

From stev: as x>0. How do you find the limit of f(x)=(sin4x)/(tan9X) Answered by Harley Weston. 





lim sin 4x/sin 6x as x approaches zero 
20080222 

From josh: lim sin 4x/sin 6x
x approachs 0 Answered by Stephen La Rocque and Harley Weston. 





lim sinx/(x +tanx) 
20071216 

From shimelis: i have problem how do you solve this equation
lim sinx/(x +tanx) Answered by Harley Weston. 





ln(x)/x 
20071207 

From Nooruddin: How can I calculate the absolute minimum of (ln x)/x? Answered by Stephen La Rocque. 





lim [x + squareroot(x^2 + 3)] as x>inf 
20071116 

From David: Find the limit. (Hint: treat the expression as a fraction whose denominator is 1, and rationalize the numerator.)
lim [x + squareroot(x^2 + 3)] as x>inf
i got to
lim 3/(x  squareroot(x^2 + 3)) as x>inf
but i'm having trouble understanding why the answer is 0 plz explain thx Answered by Harley Weston. 





A limit of the form 0 times infinity 
20071113 

From Russell: find the following limit
lim x((e^1/x) 1) as
x > infinity Answered by Penny Nom. 





lim x>1 (root x  x^2)/{1  root x) 
20071016 

From Meghan: Hi! I have a question from my Calculus textbook that I've been picking at for a while and I'm stuck.
lim x>1 (root x  x^2)/{1  root x). Answered by Stephen La Rocque and Penny Nom. 





lim (1 2 cosx) / (sin(x pi/3)) 
20071015 

From hanan: lim (1 2 cosx) / (sin(x л/3)) Answered by Harley Weston. 





A trig limit 
20071012 

From Amanda: What is the limit, as x tends to zero, of: (1cos(4x))/(xsin(x))?
Thank you!
~Amanda Answered by Harley Weston. 





The tangent to y = x^3 at x = 0 
20070904 

From Amit: consider the equation = x^3. The equation of tangent to this curve (which is smmetrical in Ist and IVth quadrant) at (0,0) is y=0, which is xaxis.
but graphically one can visulize that xaxis intersects the curve, so how can it be the tangent to the curve. Please help. Answered by Harley Weston. 





Another trig limit 
20070716 

From Richter: lim (π + x)/[cos(x/2)]
x>π Answered by Harley Weston. 





A trig limit 
20070716 

From Richter: what is the value of lim [cos (π/x)]/(x2) as x>2? Answered by Harley Weston. 





sinx and cosx 
20070625 

From Mac: Can anyone tell me whether sinx and cosx is differentiable at x=0 ?
As far as i know, cos(x) and sin(x) is differentiable at all x. Answered by Penny Nom and Stephen La Rocque. 





Limits as x approaches a constant 
20070625 

From Mac: can you please tell me what is the reason they say "denominator is a negative quantity"
in the solution 11 and "denominator is a positive quantity" solution 10 ??
If i guess correctly, for solution 10, its because of x^2 in the denominator. Answered by Penny Nom. 





The limit of a rational function 
20070528 

From Imad: 3 _______ 3 _______
lim \/ 1 + x  \/ 1  x
x>0  
x Answered by Penny Nom. 





Find the sample size needed 
20070513 

From Mini: Find the sample size needed to be 98% confident thata marketing survey on the proportion of shoppers who use the internet for holiday shopping is accurate within a margin of error of 0.02. Assume that the conditions for a binomial distribution are met, and that a current estimate for a sample proportion does not exist. Answered by Penny Nom. 





What is the limit of 3.x^(3/x) as x approaches +infinity? 
20070411 

From Teodora: What is the limit of 3.x^3/x as x approaches +infinity ? Answered by Haley Ess. 





A trig limit 
20070311 

From Lo: tan(2*x)/sin(3*x) Answered by Penny Nom. 





A limit 
20070221 

From Amanda: I have tried to work out this problem by using the properties of limits and the conjugate rule to simplify but I am not real sure how to approach the problem or what they are asking for any help would be greatly appreciated. Amanda Answered by Penny Nom. 





lim x>infinity cos x 
20061207 

From Katie: I was wondering if it was possible to find: lim x>infinity cos x Answered by Stephen La Rocque. 





A limit involving trigonometry 
20060502 

From Allie: My question is how do you solve.
lim as t goes to 0 [sin squared *3t] / t squared? Answered by Penny Nom. 





1/infinity and 1/0 
20060304 

From Evan: I was thinking the other day when i was in math class that when you divide 1 by say n you'll get 1/n. As the value of n increases the smaller the number you get. So if you divide 1/infinity would that equal zero? And if that is true then would 1/0=infinity be true also? Answered by Penny Nom. 





(x/1+x)^x 
20051023 

From A student: LIMIT x.>0 (x/1+x)^{x} how to solve it. Answered by Penny Nom. 





The value of n*tan*(180/n) tends to pi 
20050711 

From Daniel: I am 14 and i have been given a piece of maths coursework whereby a farmer has to fence off a piece of land as large as possible using 1000m of fence. I already know that the formula for working out the area of any shape of a 1000m perimeter = 500^{2}/ n*tan*(180/n), however, after some research I have found out that as the number of sides (n), tends to infinity, the n*tan*(180/n) tends to pi. Why is this? Answered by Penny Nom. 





The limit as x approaches 3 of (sqrt(x+1)2)/(x3) 
20050414 

From Abraham: What is the limit as x approaches 3 of
(sqrt(x+1)2)/(x3) Answered by Penny. 





Limits and composite functions 
20040807 

From Sue: I have two questions, one about a limit and the other about a composite function. If you could help me, I'd really appreciate it.
1. Find the limit:
lim[x>0] (x*csc(x))
I converted csc(x) to cos(x)/sin(x), but I didn't know what to do after that.
2. f(g(x)) = ln(x^2 + 4), f(x) = ln(x^2) and g(x) > 0 for all real x, find g(x):
I'm having trouble with this one because x^2 + 4 isn't a perfect square.
Sue Answered by Penny Nom. 





When is the limit of f(x) undefined? 
20040803 

From Nicolasa: When is the limit of f(x) undefined? Answered by Penny Nom. 





A sequence that converges to e 
20030316 

From Dane: Something I noticed fooling around with a calculator about 30 years ago. Considering e = 2.718281828459045.... Using Window's Calculator you will find 1.1^{11} = 2.8531167... 1.01^{101} = 2.731861... 1.001^{1001} = 2.71964085... 1.0001^{10001} = 2.71841774... 1.00001^{100001} = 2.7182954... 1.000001^{1000001}1 = 2.178231875... 1.0000001^{10000001} = 2.178219643... There apears to be a pattern. My conjecture is: 1.'infinite number of zeros'1^{1'infinite number of zeros'1} = e. Answered by Penny Nom. 





Harmonic numbers 
20030312 

From Becky: What can you tell me about the limit of harmonic numbers as it reaches infinity? Answered by Penny Nom. 





A limit 
20020903 

From Circe:
Lim 3x^{ 3}+ax+a+3 /(x^{ 2}+x2), X>2 Answered by Penny Nom. 





Asymptotes 
20011109 

From Frank:
given the function: f(x) = (x^{2}) / (x1) the correct answer to the limit of f(x) as x approaches infinity is: y = x+1 all math references point to this answer and the method they all use is long division of x1 into x^{2} however if one were to multiply both the numerator and denominator by 1/x and then take the limit, one gets: y=x how can the descrepency between the two answers be explained? Answered by Chris Fisher and Penny Nom. 





A limit using l'hopital's rule 
20001213 

From Wassim: I need to know how to solve the: limits of (x ( to the power lamda) 1 )/LAMDA when lamda tends to zero ( the answer is that the functional form is ln x) and I still don't know how using hopital rule leads to this answer. Answered by Harley Weston. 





L'Hospital's Rule 
20000719 

From Dan Krymkowski: The limit of the following as x goes to infinity is 2*y. Y is a constant. lim 2*x*log(x/(xy)) = 2*y Answered by Harley Weston. 





Central Limit Theorem and Law of Large Numbers 
20000626 

From Jonathan Yam: The Central limit Theorem states that when sample size tends to infinity, the sample mean will be normally distributed. The Law of Large Number states that when sample size tends to infinity, the sample mean equals to population mean. Is the two statements contradictory? Answered by Paul Betts and Harley Weston. 





The limit of f(x)/x 
20000122 

From Laurent Jullien: I would appreciate help to prove that a twice continuously differentiable convex function from R+ to R has the property that f(x)/x has a limit when x tends to infinity. Answered by Claude Tardif. 





l'Hospital's Rule 
19991018 

From Yannick Gigandet: How can I solve these two limits :  lim when n approches 1 of n[a^{1/n} 1]
 lim when x approches 0 of (e^{ax}  e^{bx}) / x
Thanks for the answer! Answered by Harley Weston. 





A trig limit 
19991006 

From Yannick Gigandet: What is the limit, as x approaches pi/3, of (12cosx) / sin(x(pi/3)) ? Answered by Penny Nom. 





Two limits 
19991002 

From Jennifer: How do I find lim (1cosx)/(x^2) as x> 0 and lim (tan3x)/x as x>0 Answered by Harley Weston. 





A trig limit 
19981114 

From Amy Atwell: what is the limit of of tanx / x + sin x as x approaches 0 Answered by Harley Weston. 





A trig limit 
19980528 

From Ann: This problem is a calculus 1 limit problemhigh school level. I'm teaching myself calc over the summer and I'm already stumped. find the limit lim sec^(2)[(sqrt2)(p)]1 p>0  1sec^(2)[(sqrt3)(p)] I'm Ann. Answered by Harley Weston. 





Limited area and unlimited perimeter. 
19971128 

From Rosa: There is a figure, it has unlimited perimeter but has limited area , what is the figure and how to draw it ? Thank you very much! Answered by Harley Weston. 





A Trigonometric Limit 
19970918 

From Brian Ray: What is the limit, as x approaches 0, or tan^23x/x^2? (read, tan squared 3x over...)? Answered by Harley Weston. 





A Limit Problem 
19970916 

From Robert Reny: what is the limit, as x approaches 0, of 3x/2x[x]? [] means absolute value. Answered by Harley Weston. 





A Monte Carlo Procedure 
19970423 

From Donna Hall: A irregularly shaped object of unknown area A is located in the unit square 0<=x<=1. Consider a random point uniformly distributed over the square. Let X = 1 if the point lies inside the object and X = 0 otherwise. Show that E(X) = A. How could A be estimated from a sequence of n independent points uniformly distributed over the square? How would you use the central limit theorem to gauge the probable size of the error of the estimate. Answered by Harley Weston. 





The Central Limit Theorem 
19970421 

From Donna Hall: A skeptic gives the following argument to show that there must be a flaw in the central limit theorem: We know that the sum of independent Poisson random variables follows a Poisson distribution with aparameter that is the sum of the parameters of the summands. In particular, if n independentPoisson random variables, each with parameter 1/n, are summed, the sum has a Poisson distributionwith parameter 1. The central limit theoren says the sum tends to a normal distribution, butPoisson distribution with parameter 1 is not normal. What do you think of this argument? Answered by Neal Madras. 





The normal distribution. 
19970321 

From Donna D.Hall: I am looking for a proof for the normal distribution. I suppose "proof" was not a good choice of words. What I am looking for is a way to "derive" the normal distribution in simple terms so that the most average teenager can see the logic. Can you help me? Answered by Harley Weston. 





La limite de (x(n)) 
20021001 

From Une étudiante: 3) Soit L, le point ayant pour abscisse la limite de (x(n)) a) Exprimer la distance M(n)L en fonction de n b) Déterminer le plus petit entier naturel n(o) pour lequel la distance Mn(o)L est inférieur à 0,01 c) Justifier alors qu'à partir du rang n(o), tous les points M(n) sont situés dans le segment de centre L et de rayon 0,0 1 Answered by Claude Tardif. 

