Question

Calculate the following limit:
lim
h→0
(4 + h)3− 64 over
h

Answer 1

Ok Here is your problem :
\[\Large lim h-->0 \frac{(f+h)^3-64}{h}\]

Answer 2

64=4^3

Answer 3

expand the cubic

\[\lim_{h \rightarrow 0}\frac{64 + 48h + 12h^2 + h^3 - 64}{h}\]

which simplifes to

\[\lim_{h \rightarrow 0}\frac{48h + 12h^2 + h^3}{h}\]

take out the common factor of h leaves

\[\lim_{h \rightarrow 0} 48 + 12h + h^2\]

give the limit of 48

Answer 4

Here is a Hint :
______________
Add 4 and subtract 4 from the denominator :
it will be
\[\Large \frac{(4+h)^3-4^3}{(4+h)-4}\]
Now its easy :
The answer is 3/1*4^(3-1)=48

Answer 5

thanks yall