If f(x) = 3x^2 - 8x^-2, then!!!!!!!!!!!!!!!!!!!!!!!!!!!

Question

then lim as h approaches 0 f(2+h) - f(2) all over h =

Answer 1

The function f(x) = 3x² - 8x^{- 2} .

f(2) = 3(2)² - 8(2)^{- 2} = 12 - 2 = 10.

f(2 + h) = 3(2 + h)² - 8(2 + h)^{- 2} .

lim [ f(2 + h) - f(2) ] = lim [ 3(2 + h)² - 8(2 + h)^{- 2} - 10]

h ---> 0                   h ---> 0

Allpy limits.

Substitute 0 for h.

= 3(2 + 0)² - 8(2 + 0)^{- 2} - 10

= 3(2)² - 8(2)^{- 2} - 10

= 12 - 2 - 10

= 12 - 12

= 0.

Therefore, lim [ f(2 + h) - f(2) ] = 0.

                  h ---> 0