lim h → 0 (f(2+h)-f(2))/h

F(x)=x^2+1

Question

lim h → 0    (f(2+h)-f(2))/h

F(x)=x^2+1

anonymous · Answer

4
and in a week you will do this problem in your head in two seconds by saying "the derivative of 
$$x^2+1$$ is 
$$2x$$ and 
$$2\times 2=4$$ but you have not gotten there yet so you have some work to do

anonymous · Answer

Could you please show work on how to solve this using the equation, so I know for future refrences?

anonymous · Answer

$$f(2)=2^2+1=5$$
$$f(2+h)=(2+h)^2+1=4+4h+h^2+1=5+4h+h^2$$
$$f(2+h)-f(2)=5+4h+h^2-5=4h+h^2$$
$$\frac{f(2+h)-f(2)}{h}=\frac{4h+h^2}{h}=\frac{h(4+h)}{h}=4+h$$

anonymous · Answer

now you can take the limit as h goes to zero and you get 4 for sure

anonymous · Answer

all steps are there, nothing left out

anonymous · Answer

WOW thank you!

anonymous · Answer

yw
notice that the 5's add to zero. it will always work this way if the limit exists. because you have an h in the denominator, the only way for this limit to exist is if the constant goes and you have nothing but h's