Calculus problem

Question

Find 

Options:

1. 6x
2. 3x² + h² +7
3. 3x² + 7
4. 6x + 7

Answer 1

To do a problem like this, take one step at a time:

Lim (as h -> 0) [ ( 3 (x + h)² + 7) -  ( 3 x² +7) ]/h                 (I believe this is the equation you meant.)

Lim (as h -> 0) [ (3 ( x² + 2xh + h²) + 7) – ( 3 x² +7) ]/h     (Squared (x + h))

Lim (as h -> 0) [ (3 x² + 6xh + 3h²) + 7) – ( 3 x² +7) ]/h     (Distributed the 3)

Lim (as h -> 0) [ (3 x² + 6xh + 3h² + 7 – 3 x² - 7) ]/h          (Took the parentheses off (& distributed the “-“)

Lim (as h -> 0) [ 6xh + 3h² ]/h                                             (Cancelled Terms)

Lim (as h -> 0) [ 6x + 3h]                                                    (Cancelled h from the numerator & denominator)

= 6x                                                                                     (as h goes to 0, 3h goes to zero, so limit is 6x+0.)