college calculus
posted by Anonymous .
use the definition of derivative to prove that
lim x>0 [ln(1+x)]/[x] = 1

[ln (u + h)  ln (u)]/h as h>0= definition of d/du(ln u) = 1/u
here u = 1
so
1/1 = 1
Respond to this Question
Similar Questions

calculus again
Suppose lim x>0 {g(x)g(0)} / x = 1. It follows necesarily that a. g is not defined at x=0 b. the limit of g(x) as x approaches equals 1 c.g is not continuous at x=0 d.g'(0) = 1 The answer is d, can someone please explain how? 
calculus plz heLP
can someone please prove the difference rule to me? 
Calculus  need help!
Use the definition of the derivative to find f'(x) 1. f(x) 2x^2 + x  1 Before the final step, my 'result' looked weird and I think I did something wrong in my arithmetic...someone correct me? 
calculus
Need help with the following proof: prove that if lim x>c 1/f(x)= 0 then lim x>c f(x) does not exist.I think i need to use the delta epsilon definition i am not sure how to set it up. 
Maths Calculus Derivatives & Limits
Using the definition of the derivative evaluate the following limits 1) Lim h> 0 [ ( 8 + h )^1/3  2 ] / h 2) Lim x > pi/3 ( 2cosx  1 ) / ( 3x  pi) 
Calculus
I have two similar problems that I need help completing. Please show all your work. Question: Find the limit L. Then use the åä definition to prove the limit is L. 1. lim (2x+5) x>3 2. lim 3 x>6 Thank you for your anticipated … 
Calculus
I know the derivative of x is 1, but I'm having a hard time proving it with the limit definition of the derivative. I have... Lim delta x >0 (x+ delta x)(x)/delta x = 0 But I know the answer is 1. I don't understand what I am … 
Calculus
I don't know limits fairly well. The problem is prove the limit using definition 6, lim x > 3, 1 / (x+3)^4 = infinity. The books definition for definition 6 is, let f be a function defined on some open interval that contains a, … 
calculus
Use the definition of derivative: lim(as h approaches 0) (f(x+h)f(x)/(h) to find f(x)=(1)/(2x). 
Math  Calculus
f(x) = { x^2sin(1/x), if x =/= 0 0, if x=0} a. find lim(x>0)f(x) and show that f(x) is continuous at x=0. b, find f'(0) using the definition of the derivative at x=0: f'(x)=lim(x>0) (f(x)f(0)/x) c. Show that lim(x>0)f'(x) …