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 Topic: limit
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 The limit of (e^x-1)^(1/x) as x tends to 0 2018-02-27 From ARGHA:Find the limit of (e^x-1)^(1/x) as x tends to 0.Answered by Penny Nom. A limit 2017-05-14 From Soham:Find out the value of the following: lim (x+x^2 +x^3 +.........x^n–n)/(x–1) x→1Answered by Penny Nom. A tolerance limit is 0.5% 2017-01-06 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 JoeAnswered by Penny Nom. A limit of a rational function 2016-01-16 From selvamani:F (x) = x^3+3x^2-9x-2 / x^3-x-6 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 2015-03-13 From arthur:sin(x-1)/x^+x-2Answered by Penny Nom. A limit 2015-02-19 From genc:Lim (27x^3-1) / (3x-1) X-> 1/3Answered by Harley Weston. A limit with trig functions 2014-02-22 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? 2013-02-13 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 2012-04-02 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=kIq5CZlg8RgAnswered by Robert Dawson. A limit 2012-01-18 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 2011-12-30 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 functionAnswered by Penny Nom. The derivative of f(x) = (x+1)^1/2 2011-09-05 From Carla:Find the derivative using the limit process of f(x) = (x+1)^1/2Answered by Harley Weston. limit as x approaches a of ((x^(1/2))-(a^(1/2)))/(x-a)? 2010-09-29 From emily:limit as x approaches a of ((x^(1/2))-(a^(1/2)))/(x-a)?Answered by Penny Nom. A limit 2010-09-27 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 / x-a if x is not = a          {6 if x = aAnswered by Penny Nom. Limits 2010-09-20 From rodrigo:what's the limit of x+1/x-1, when x tends to 1?Answered by Janice Cotcher. Using the limit definition 2010-06-06 From Meagan:Using the limit definition find the derivative of 3/(2x^2)Answered by Harley Weston. The derivative using limits 2009-04-21 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 2009-03-06 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, JustinAnswered by Robert Dawson and Harley Weston. A trig limit 2009-02-05 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 2009-02-05 From Kathy:Hi! I was just wondering how to do this question: lim 1-cos2x/xsinx as x approaches 0 Thanks, KathyAnswered by Penny Nom. limit sinx/x 2009-01-30 From Jackie:how to evaluate limit sinx/x as x tends to zero if x is in degreesAnswered by Stephen La Rocque and Harley Weston. Limit of a Trig Function 2008-12-06 From Berta:Evaluate limit xcsc2x/cos 5x as x goes to 0 ans is 2 but I get 1/2 x/sin2xcos5x = 2x/2sin2xcos5x= 1/2cos5xAnswered by Penny Nom. A trig limit 2008-11-04 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 2008-09-16 From Brooks:what is the limit as x approaches 10 for f(x) = sqrt(x-1) = 3 pleeeeeaase help me out hereAnswered by Janice Cotcher. Right Sided Limit of an Exponential Function 2008-07-29 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 2008-07-29 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 x-cosx/x x->ooAnswered by Harley Weston. limit x->0 (logx-log(x-1)) 2008-05-22 From kritica:lt x->0 (logx-log(x-1))Answered by Harley Weston. lim as x approaches infinite of 5x + 2/x-1 2008-04-04 From Jordan:how to solve this. lim as x approaches infinite of 5x + 2/x-1Answered by Stephen La Rocque and Harley Weston. The limit of (sin4x)/(tan9x) as x approaches zero 2008-03-14 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 2008-02-22 From josh:lim sin 4x/sin 6x x approachs 0Answered by Stephen La Rocque and Harley Weston. lim sinx/(x +tanx) 2007-12-16 From shimelis:i have problem how do you solve this equation lim sinx/(x +tanx)Answered by Harley Weston. ln(x)/x 2007-12-07 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 2007-11-16 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 thxAnswered by Harley Weston. A limit of the form 0 times infinity 2007-11-13 From Russell:find the following limit lim x((e^1/x) -1) as x --> infinityAnswered by Penny Nom. lim x->1 (root x - x^2)/{1 - root x) 2007-10-16 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)) 2007-10-15 From hanan:lim (1- 2 cosx) / (sin(x- л/3))Answered by Harley Weston. A trig limit 2007-10-12 From Amanda:What is the limit, as x tends to zero, of: (1-cos(4x))/(xsin(x))? Thank you! ~AmandaAnswered by Harley Weston. The tangent to y = x^3 at x = 0 2007-09-04 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 x-axis. but graphically one can visulize that x-axis intersects the curve, so how can it be the tangent to the curve. Please help.Answered by Harley Weston. Another trig limit 2007-07-16 From Richter:lim (π + x)/[cos(x/2)] x-->-πAnswered by Harley Weston. A trig limit 2007-07-16 From Richter:what is the value of lim [cos (π/x)]/(x-2) as x-->2?Answered by Harley Weston. sin|x| and cos|x| 2007-06-25 From Mac:Can anyone tell me whether sin|x| and cos|x| 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 2007-06-25 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 2007-05-28 From Imad:     3 _______ 3 _______ lim \/ 1 + x -    \/ 1 - x x->0 ---- ----------------------------               xAnswered by Penny Nom. Find the sample size needed 2007-05-13 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? 2007-04-11 From Teodora:What is the limit of 3.x^3/x as x approaches +infinity ?Answered by Haley Ess. A trig limit 2007-03-11 From Lo:tan(2*x)/sin(3*x)Answered by Penny Nom. A limit 2007-02-21 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. AmandaAnswered by Penny Nom. lim x-->infinity cos x 2006-12-07 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 2006-05-02 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 2006-03-04 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 2005-10-23 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 2005-07-11 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 = 5002/ 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)/(x-3) 2005-04-14 From Abraham:What is the limit as x approaches 3 of (sqrt(x+1)-2)/(x-3)Answered by Penny. Limits and composite functions 2004-08-07 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. --SueAnswered by Penny Nom. When is the limit of f(x) undefined? 2004-08-03 From Nicolasa:When is the limit of f(x) undefined?Answered by Penny Nom. A sequence that converges to e 2003-03-16 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 1.111 = 2.8531167... 1.01101 = 2.731861... 1.0011001 = 2.71964085... 1.000110001 = 2.71841774... 1.00001100001 = 2.7182954... 1.00000110000011 = 2.178231875... 1.000000110000001 = 2.178219643... There apears to be a pattern. My conjecture is: 1.'infinite number of zeros'11'infinite number of zeros'1 = e. Answered by Penny Nom. Harmonic numbers 2003-03-12 From Becky:What can you tell me about the limit of harmonic numbers as it reaches infinity?Answered by Penny Nom. A limit 2002-09-03 From Circe: Lim 3x 3+ax+a+3 /(x 2+x-2), X->-2 Answered by Penny Nom. Asymptotes 2001-11-09 From Frank: given the function: f(x) = (x2) / (x-1) 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 x-1 into x2 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 2000-12-13 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 2000-07-19 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/(x-y)) = 2*y Answered by Harley Weston. Central Limit Theorem and Law of Large Numbers 2000-06-26 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 2000-01-22 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 1999-10-18 From Yannick Gigandet:How can I solve these two limits : lim when n approches 1 of n[a1/n -1] lim when x approches 0 of (eax - ebx) / x Thanks for the answer!Answered by Harley Weston. A trig limit 1999-10-06 From Yannick Gigandet:What is the limit, as x approaches pi/3, of (1-2cosx) / sin(x-(pi/3)) ? Answered by Penny Nom. Two limits 1999-10-02 From Jennifer:How do I find lim (1-cosx)/(x^2) as x-> 0 and lim (tan3x)/x as x->0Answered by Harley Weston. A trig limit 1998-11-14 From Amy Atwell:what is the limit of of tanx / x + sin x as x approaches 0 Answered by Harley Weston. A trig limit 1998-05-28 From Ann:This problem is a calculus 1 limit problem-high 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 --------------------- 1-sec^(2)[(sqrt3)(p)] ` I'm Ann.Answered by Harley Weston. Limited area and unlimited perimeter. 1997-11-28 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 1997-09-18 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 1997-09-16 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 1997-04-23 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 1997-04-21 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 a parameter that is the sum of the parameters of the summands. In particular, if n independent Poisson random variables, each with parameter 1/n, are summed, the sum has a Poisson distribution with parameter 1. The central limit theoren says the sum tends to a normal distribution, but Poisson distribution with parameter 1 is not normal. What do you think of this argument?Answered by Neal Madras. The normal distribution. 1997-03-21 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)) 2002-10-01 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.

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