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

1. anonymous

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

2. anonymous

64=4^3

3. campbell_st

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

4. anonymous

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

5. anonymous

thanks yall