Finding limit using l'Hopitals rule

  • Thread starter Thread starter fran1942
  • Start date Start date
  • Tags Tags
    Limit
fran1942
Messages
80
Reaction score
0
Hello, I am tying to use l'Hopital's rule to solve this limit:
{e^(5+h)-e^5} / h
limit h tending towards 0

Using l'Hopitals rule I differentiate both numerator and denominator to get:
e^(5+h)-e^5 / 1
THen plugging 0 back in I get 0/1 which would give me a limit of 0 ?
But I think the limit should actually be e^5.

Can someone see where I have gone wrong ?
Thanks kindly
 
Last edited:
Physics news on Phys.org
fran1942 said:
Hello, I am tying to use l'Hopital's rule to solve this limit:
e^(5+h)-e^5 / h
limit h tending towards 0

Using l'Hopitals rule I differentiate both numerator and denominator to get:
e^(5+h)-e^5 / 1
THen plugging 0 back in I get 0/1 which would give me a limit of 0 ?
But I think the limit should actually be e^5.

Can someone see where I have gone wrong ?
Thanks kindly
What is the rate of change of e^5 with respect to h? I am assuming you are dealing with { e(5+h) - e^5 }/h.
 
Last edited:
RoshanBBQ said:
What is the rate of change of e^5 with respect to h? I am assuming you are dealing with { e(5+h) - e^5 }/h.

yes, that is correct. I am trying to apply l'Hopital's rule to that formula to obtain the limit as h tends towards 0.
I don't think I have it right in my attempt above. Any help would be appreciated.

Thank you.
 
fran1942 said:
Hello, I am tying to use l'Hopital's rule to solve this limit:
{e^(5+h)-e^5} / h
limit h tending towards 0

Using l'Hopitals rule I differentiate both numerator and denominator to get:
e^(5+h)-e^5 / 1
THen plugging 0 back in I get 0/1 which would give me a limit of 0 ?
But I think the limit should actually be e^5.

Can someone see where I have gone wrong ?
Thanks kindly

e^5 is a constant. What's the derivative of a constant?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

L'Hopital's Rule case: How does x^(-4/3) equal 0 when x approches infinity?
Replies
1
Views
1K
What is my mistake in solving for this limit?
Replies
23
Views
2K
Solving Limits & L'Hopital w/ A & B Parameters
Replies
21
Views
2K
Determine limits of integration in double integral change of variables
Replies
2
Views
1K
Limit of (-x^(k+1))/e^x: Solving Step by Step with l'Hopital's Rule
Replies
5
Views
2K
Prove that the limit as n->infinity of n^n/n! is infinity
Replies
7
Views
1K
Limit of a fraction as n-> infinity in the numerator and denomominator
Replies
17
Views
2K
Verify a limit using L'Hopital's Rule
Replies
14
Views
2K
Solving a limit by l'hopital's rule
Replies
9
Views
2K
How should I use the averaging approximation to find this?
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top