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28 items are filed under this topic.
A limit 2015-03-13
From arthur:
Answered by Penny Nom.
A limit 2015-02-19
From genc:
Lim (27x^3-1) / (3x-1)
X-> 1/3

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=kIq5CZlg8Rg

Answered by Robert Dawson.
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 function
Answered by Penny Nom.
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!



Answered 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



Answered 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.
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! ~Amanda
Answered 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.
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.
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.
A trig limit 2007-03-11
From Lo:
Answered by Penny Nom.
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.


Answered 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.
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.
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:


how can the descrepency between the two answers be explained?

Answered by Chris Fisher and Penny Nom.
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.
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 :
  1. lim when n approches 1 of n[a1/n -1]

  2. lim when x approches 0 of (eax - ebx) / x
Thanks for the answer!

Answered by Harley Weston.
Two limits 1999-10-02
From Jennifer:
How do I find

lim (1-cosx)/(x^2) as x-> 0


lim (tan3x)/x as x->0
Answered 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.



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