Question

lim (h->0) [(10+3)^3-1000]/h =

Answer 1

i meant (10+h)^3

Answer 2

(10+h)^3
=10^3+3*10^2*h+3*10*h^2+h^3
=10^3+3*10*h(10+h)+h^3
=1000+30h(10+h)+h^3
=1000+300h+30h^2+h^3
=h^3+30h^2+300h+1000

Answer 3

thanks

Answer 4

\[\lim_{h\rightarrow 0}\frac{(10+h)^3-1000}{h}=\lim_{h\rightarrow 0}\frac{(10+h)^3-10^3}{(10+h)-10}=f'(10)\]\[f(x)=x^3\quad,\quad f'(x)=3x^2\quad\Rightarrow\quad f'(10)=300\]