Homework Statement
For which value of d does the following limit exist?
lim x->d ln [ (x2-13x+30) / (x-d) ]
Homework Equations
None
The Attempt at a Solution
I understand how to find limits when the limit goes to a real number, and has a variable in the function to solve for, but not when...
Homework Statement
can you cancel the x and the |x|[/B]
lim x→0 ( x(1-(cos(x))/|x| )
2. Homework Equations
The Attempt at a Solution
At first i thought the limit would just be undefined as x approaches 0 but the answer to the problem is actually 0, so can you just cancel the x with the...
Homework Statement
Homework Equations
The Attempt at a Solution
I think this problem is probably a lot simpler than I am making it out to be. However, when I apply sterling's approx., I get a very nasty equation that does not simplify easily.
One of the biggest problems I have though is...
Does 0.999... equals 1?
I know that this is a very basic well known concept but recently I stumbled across a video on Youtube in which the creator argues that the two are not equivalent
I posted a comment arguing that in the case of Infinite sum of Σn=0 9(1/10)n you can find the sum of the...
Homework Statement
lim as x tends to -∞ (x)^3/5 - (x)^1/5
Homework Equations
The Attempt at a Solution
The first thing I did was convert it into a radical so it becomes fifthroot√x^3 - fifthroot√x.
Then I rationalized to get ( x^3-x)/(fifthrt√x^3+fifthroot√x) . I then divided the top by...
1. Problem statment
Q. Use limit to find the instantaneous velocity at time t if the postition is p(t) at time t.
p(t) = t + (1/t) at x = t
2. Homework Equations
(Sorry dashes are in there to keep everything where it should be. I don't know how to make fractions in this and it was...
Hi!
First time poster, I'm about to enter first year calc and thought that I could get ahead of the curve by checking out some questions beforehand. This showed up on one of the university calculus exams but I couldn't figure out how to do it. I tried to finding a common denominator but then was...
I have found that multivariable limits are harder to find and/or prove that something exists.
Do you have any recommendations, given questions like "find(if exists) the limit....".
For example, I have no idea how to even start thinking about the following limit(if it exists or not, and if it...
Homework Statement :
the question wants me to prove that the limit of f(x,y) as x approaches 1.3 and y approaches -1 is (3.3, 4.4, 0.3). f(x,y) is defined as (2y2+x, -2x+7, x+y).
[/B]
The attempt at a solution: This is the solution my lecturer has given. it's not very neat, sorry...
Hello,
I am want to prove that: $$ \sum_{1}^{\infty} \frac{1}{n^{2} + 1} < \frac{1}{2} + \frac{1}{4}\pi $$
Cauchy's Convergence Integral
If a function decreases as n tends to get large, say f(x), we can obtain decreasing functions of x, such that:
$$ f(\nu - 1) \geqslant f(x) \geqslant...
Homework Statement
Hey guys. I am having a little trouble answering this question. I am teaching myself calc 3 and am a little confused here (and thus cant ask a teacher). I need to find the limit as (x,y) approaches (0,1) of f(x,y) when f(x,y)=(xy-x)/(x^2+y^2-2y+1).
Homework Equations...
Homework Statement
\lim\limits_{x \to 0} \left(\ln(1+x)\right)^x
Homework Equations
Maclaurin series:
\ln(1+x) = x - \frac{x^2}{2} + \frac{x^3}{3} + ... + (-1)^{r+1} \frac{x^r}{r} + ...
The Attempt at a Solution
We're considering vanishingly small x, so just taking the first term in the...
Homework Statement
Determine which of the sequences converge or diverge. Find the limit of the convergent sequences.
1) {asubn}= [((n^2) + (-1)^n)] / [(4n^2)]
Homework Equations
[/B]
a1=first term, a2=second term...an= nth term
The Attempt at a Solution
a) So I found the first couple of...
Hi I was wondering how you get this when taking the limit of T going to 0
From this expression of S:
Please help I don't see how ln infinity goes to uB/KbT (used u to represent the greek letter. And how does the other expression of sinh and cosh approach 1?
Homework Statement
I have to determine whether or not the following sequence is convergent, and if it is convergent, I have to find the limit.
an = (-2)n / (n!)
In solving this problem, I am not allowed to use any form or variation of the Ratio Test.
2. The attempt at a solution
I was...
Homework Statement
Evaluate or show that the limit does not exist:
\lim_{(x,y) \to (0,0)}\frac{ 2x^{4} + 5y^{3} }{8x^{2}-9y^{3}}
\lim_{(x,y) \to (0,-2)}\frac{ xy+2x }{3x^{2}+(y+2)^{2}}
Homework Equations
The Attempt at a Solution
So the first one is indeterminate and cannot be...
Homework Statement
I need to see if the function defined as
##f(x,y) = \left\{
\begin{array}{lr}
\frac{xy^2}{x^2 + y^2} & (x,y)\neq{}(0,0)\\
0 & (x,y)=(0,0)
\end{array}
\right.##
is differentiable at (0,0)
Homework Equations
[/B]
A function is differentiable at a...
hi I don't understand how to do one type of homework problem, here's an example of the type:
If limit of f(X)/X = 1 as X ->0 evaluate the limit f(X) as X->0
Homework Statement
f(x)=-2 when x<1
=3 when x=1
=x-3 when x>1
find the limit at 1 from the left and right sides and at 1.
Homework Equations
The Attempt at a Solution
limit for x when approaching 1 from the left is -2
limit for x when approaching 1 from the right is -2
-I'm not...
Homework Statement
If k is a positive integer, then show that
##\lim_{x\to\infty} (1+\frac{k}{x})^x = \lim_{x\to 0} (1+kx)^\frac{1}{x}##
Homework Equations
L'Hopitals rule, Taylor's expansion
The Attempt at a Solution
How should I begin? Should I prove that both has the same limit, or is...
This was just very basic, I have accepted it in just a heartbeat, but when I tried to chopped it and examined one by one, somethings fishy is happening, this just involved \int_{0}^{\infty}x e^{-x}dx=1.
Well, when we do Integration by parts we will have let u = x du = dx dv = e^{-x}dx v =...
I have been playing around with calculus for a while and I wondered what would it be like to make some changes to the definition of derivatives.
I'd like to look at the original definition of derivatives in this way (everything is in lim Δx→0):
F(x+Δx) - F(x) = F'(x) * Δx
The Δx factor...
Homework Statement
Consider the sequence given by b_{n} = n - \sqrt{n^{2} + 2n}. Taking (1/n) \rightarrow 0 as given, and using both the Algebraic Limit Theorem and the result in Exercise 2.3.1 (That if (x_n) \rightarrow 0 show that (\sqrt{x_n}) \rightarrow 0), show \lim b_{n} exists and find...
Homework Statement
From Spivak: Suppose that ##A_{n}## is, for each natural number ##n##, some finite set of numbers in ##[0,1]##, and that ##A_n## and ##A_m## have no members in common if ##m\neq n##. Define f as follows:
##f(x) = \frac{1}{n}##, if ##x \in A_n##
##f(x) = 0##, if ##x \notin...
Hi,
I know that when you take this limit it is equal to e^-wo, but I was just wondering how you got there when taking the limit?
lim w-->wo ((exp(w)-exp(wo))/(w-wo))^-1 = 1/e^wo
w and wo are both two points within the same plane.
Homework Statement
Evaluate ##\lim_{x\to 0} \frac{2^x-1-x\log_e2}{x^2}## without using L'Hospital's rule or expansion of the series.
Answer is given to be = ##\frac{(\log_e (2))^2}{2}##
Homework Equations
Squeeze play theorem/ Sandwich theorem, some algebraic manipulations and standard...