# limit

1. ### I cannot seem to fine G(x) within the formula, it seems pretty simple.

We want to calculate the limit. limx→∞4x23x4+2−−−−−−√ . Rewrite 4x23x4+2−−−−−−√ as 43+g(x)−−−−−−−√ where g(x)= ?
2. ### Limit calculation

In the image below, how am I applying the limit laws wrong? I know the correct solution is 5, but I get -1! The problem I am facing is something related to my usage of the product rule for limits.
3. ### Calculating limit of rational function

For the question in the image, can someone please explain to me why we should interpret $\sqrt{x^2}$ as $|x|$?
4. ### Proving inequality for all values greater than n0

Hi, I hope someone can help. I'm trying to figure out how to formally prove that $$\log_2(n) - \log_{10}(n) \geq \frac{\log_2(n)}{2^n}$$ I know intuitively that the right-hand side will become 0 for very large values of n, and the left-hand side will be increasing, but I am not sure how to...
5. ### Find the slope of the tangent line on f at x=1

So I'm studying for my first calculus exam, and this problem has me stumped for hours now. I've used the formula of lim h-->0 f(x+h)-f(x) / h It becomes so complicated and confusing as I try to multiply by the conjugate to remove the radicals in the numerator, it just never simplifies to a...
6. ### Limit question

Determine the value of a so that $f(x) = \frac{x^2+ ax + 5}{x+1}$has a slant asymptote y = x + 3
7. ### Please explain why marks were taken off in this limit question

My teacher said I have to solve all the limits at once, but I don't understand why it matters if I solve one before the other. Can someone please explain why this is wrong?
8. ### Derivatives and limits

Hi, I hope someone can help. I want to know whether my thinking is right or not about the following question: For 15a - Not exactly sure how to interpreted this one and would really appreciate help on this. For 15 b - I interpreted this limit as the derivative for e^x at x = 2, which...
9. ### Differentiability implies continuity question

Hi, So I'm trying to fully understand the theorem that suggests if "f" is differentiable at "a", then "f" is continuous at "a". The issue that i'm facing with this definition is when I'm dealing with function which have holes in them, such as f(x) = (x^2-4)/(x-2) which then simplify's to f(x)...
10. ### Use of Calculus

What is the use of calculus in computer engineering. we study math in computer like boolean algebra,general math for programming but what computer does with calculus?(Clapping)
11. ### Proof that A^n < N!

For any positive integer A, there is an integer N, which of course can vary depending on A, so that for all n >= N, A^n < n!. How am I supposed to show this? Do I need to show A^n = Big-O of n! or use induction? I tried both and I can't seem to figure it out.
12. ### L'Hopital's Rule on an Absolute Value function. Two different answers?

Suppose there is a function, k, which is equal to . Now suppose I take the limit as n approaches infinity, so that . Now, I am at a crossroads. Do I: A)keep the absolute value bars and simply evaluate the limit of the function inside them? Or; B)remove the absolute values since we know...
13. ### find the limits, HELP

1.$\lim_{x\rightarrow 1}\frac{\sqrt{x^{2}}-2\sqrt{x}+1}{(x-1)^{2}}$ 2.$\lim_{x \rightarrow 1}\frac{\sqrt{x}-1}{\sqrt{x}-1}$ 3.$\lim_{x \rightarrow 0}\frac{\sqrt{1+x}-\sqrt{1-x}}{x}$ thank you if u take the time to solve them, means a lot!!(Bigsmile)
14. ### Solve the limit

lim √x-8/∛x-8 ×→64
15. ### Limit of Infinity

limit -x^5 + x - 1 as x goes to infinity Can I add infinity? -(infinity)^5 + infinity - 1 = -infinity + infinity (is it now positive or negative infinity?)
16. ### Limit of Infinity for Exponential Absolute Function

Find the indicated limit. lim as x goes infinity of |(x + 1) / (x - 2)|^(x^2 - 4)^(1/2)
17. ### More limit problems :( exam tomorrow!

Hi guys Can anyone please help me with a process to work out limits where an is involved. For example, 1) 2n - 1 / 5n+ 1 2) 2n + 3 / 3n+ 2 I understand that if these were problems involving x2 or x3 for example, dividing top and bottom by the highest power would be the method. Is there a...
18. ### The Absolute Value of a Number

lim 5x/(x^2 + 9)^1/2 as x goes to -4 = -20/|5| The square root of 25 could be +5 or -5. How do I decide now if the absolute of 5 is positive or negative?
19. ### Does Not Exist Limits

Can I answer DNE limits as infinity or negative infinity? like this lim sin(x) as x goes to infinity = infinity? lim sin(x) as x goes to -infinity = -infinity?
20. ### help find a and b in a limit equation

find the value of a and b