# Find the limit

posted by .

Compute lim f(2+h)-f(2)
h->0 ---------
h

• Find the limit -

did you mean
Compute lim( f(2+h)-f(2) )/h as h ---> 0 ?

If so, then this has the appearance of attempting to find the derivative of f(x) = x by First Principles when x = 2

Short way is to know that
f ' (x) = 1 , and so the result would be 1

long way:
lim( f(2+h)-f(2) )/h as h ---> 0
= lim ( x + h - x)/h as h --> 0
= lim h/h
= 1

## Similar Questions

1. ### calc

need to find: lim as x -> 0 of 4(e^2x - 1) / (e^x -1) Try splitting the limit for the numerator and denominator lim lim x->0 4(e^2x-1) (4)x->0 (e^2x-1) ______________ = ________________ lim lim x->0 e^X-1 x->0 e^x-1 …
2. ### survey of clac

g(x)={x+6, for x<-2, -1/2x+1, for x> or equal to -2, find the limit: lim g(x)= lim g(x)= x-->-2^- x-->-2^+ lim g(x)= lim g(x)= x-->-2^+ x-->4^-
3. ### Calculus

Sorry for posting another quesiton..; f(x) = { -7x^2 + 7x for x<=0 { 3x^2 + 7x for x>0 According to the definition of derivative, to compute f'(0), we need to compute the left-hand limit lim x-> 0− = _____ and the right-hand …
4. ### Calculus

Find the positive integers k for which lim ->0 sin(sin(x))/x^k exists, and then find the value the limit. (hint:consider first k=0, then k=1. Find the limit in these simple cases. Next take k=2 and finally consder k>2 and find …
5. ### Calculus

Find the indicated limits. If the limit does not exist, so state, or use the symbol + ∞ or - ∞. f(x) = { 2 - x if x ≤ 3 { -1 + 3x - x^2 if x > 3 a) lim 3+ f(x) x->3 b) lim 3- f(x) x->3 c) lim f(x) x->3 …
6. ### Calculus

Find the indicated limits. If the limit does not exist, so state, or use the symbol + ∞ or - ∞. f(x) = { 2 - x if x ≤ 3 { -1 + 3x - x^2 if x > 3 a) lim 3+ f(x) x->3 b) lim 3- f(x) x->3 c) lim f(x) x->3 …
7. ### calc

Use L’Hopital’s rule to find the limit of this sequence (n^100)/(e^n) ...If you do L'Hop. Rule it would take forever, right?
8. ### Calculus

I have two similar problems that I need help completing. Please show all your work. Question: Find the limit L. Then use the å-ä definition to prove the limit is L. 1. lim (2x+5) x->3 2. lim 3 x->6 Thank you for your anticipated …