Posted by Yousef on Tuesday, October 25, 2011 at 9:19am.
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)

Maths Calculus Derivatives & Limits  Steve, Tuesday, October 25, 2011 at 10:25am
Drag out L'Hospital's Rule
1) 1/3 (8+h)^(2/3) / 1
= 1/3 * 1/4 = 1/12
2) 2sinx/3 = √3/3

Maths Calculus Derivatives & Limits  Steve, Tuesday, October 25, 2011 at 10:26am
Oops. Using definition of derivative.
Check back later. Lots of messy algebra.

Maths Calculus Derivatives & Limits  Steve, Tuesday, October 25, 2011 at 10:48am
Use the binomial theorem to expand (8+h)^{1/3}
(8+h)^{1/3}  2 = 8^{1/3} + 1/3 8^{2/3}h  1/3 * 2/3 8^{5/3}h^{2} + ...
= 2 + 2 + 1/3 * 1/4 h  2/9 * 1/32 h^{2} + ...
Divide by h and all the terms with h^{2} or higher go away, leaving only:
1/3 8^{2/3} = 1/12
Answer This Question
Related Questions
 math  i need some serious help with limits in precalc. here are a few ...
 Calculus (Derivatives)  What is the derivative of the this functon? g(x) = 500...
 Calculus  Find the following limits algebraically or explain why they donâ€™t ...
 Calculus  F(x)=x5 evaluate the following limits lim x>5 ( f(x)f(5))/(x...
 Calculus 1  Evaluate the following limits after identifying the indeterminate ...
 calculus  Evaluate the following limits after identifying the indeterminate ...
 Maths (limits)  how do i evaluated these limits: lim x > 3 ((square root ...
 Calc Limits  lim (1+x)^1/x. Give an exact answer. x>0 This reads: The ...
 math  Evaluate the following limits: (I) Lim. (x+1)/[1sqrt(4+3x)] X >1 (II...
 math  Evaluate the following limits: (I) Lim. (x+1)/[1sqrt(4+3x)] X >1 (II...
More Related Questions