Question

Find, picture provide below

Answer 1

C. 2916

Explanation:

The given limits is

`\lim_(h \to 0) (f(9+h)-f(9))/(h)`

if
`f(x)=x^4`.

`\Rightarrow f(9)=9^4=6561`

`f(h+9)=(h+9)^4=h^4+36 h^3+486 h^2+2916 h+6561`

Our limit becomes;

`\lim_(h \to 0) (f(h+9)-f(9))/(h)= \lim_(h \to 0) (h^4+36 h^3+486 h^2+2916 h+6561-6561)/(h)`

This simplifies to;

`\lim_(h \to 0) (f(h+9)-f(9))/(h)= \lim_(h \to 0) (h^4+36 h^3+486 h^2+2916 h)/(h)`

`\lim_(h \to 0) (f(h+9)-f(9))/(h)= \lim_(h \to 0) h^3+36 h^2+486 h+2916`

`\lim_(h \to 0) (f(h+9)-f(9))/(h)= (0)^3+36 (0)^2+486(0)+2916`

`\lim_(h \to 0) (f(h+9)-f(9))/(h)= 2916`

the correct choice is C.