SNEAKY LIMITS

Lazy Lulu was examining the following limit. She recognized that this is the definition of the derivative as a limit.

$\lim\limits _ { h \rightarrow 0 } \large\frac { ( 5 ( x + h ) ^ { 2 } - 11 ( x + h ) + 7 ) - ( 5 x ^ { 2 } - 11 x + 7 ) } { h }$

1. What is the equation of $f$?

   Answer (a):

   $f(x) = 5x^2 − 11x + 7$

2. Use the Power Rule to write an equation for $f ^\prime$.

   Hint (b):

   Aren't you glad that you do not have to algebraically evaluate this limit!

3. Evaluate $\lim\limits _{ h \rightarrow 0 } \large\frac { ( 5 ( 1 + h ) ^ { 2 } - 11 ( 1 + h ) + 7 ) - ( 1 ) } { h }$. Explain what your answer represents.

   Hint (c):

   Substitute.