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Here are all the questions I have absolutely NO idea how to do.

1.

Let:

f(X) = -6x^2+6x for x<0 and 7x^2-3 for x≥ 0

According to the definition of derivative, to computer f'(0), we need to compute the left hand limit

lim x-->0- =

and the right hand limit

lim x--> 0+

We conclude that f'(0)=

So...

I've figured out that the right hand limit is

[7x^2-3-(7(0)^2-3)]/(x-0)

and that f'(0)=DNE

My answer for the left hand limit is

[-6x^2+6x-(-6(0)^2+6(0))]/(x-0)

but the website won't accept my answer.

2.

Given the following table:

x----- 0.0097 ------- 0.0098 -------- 0.0099 -------- 0.01---- 0.0101 ----- 0.0101

f(x)-- 0.54783494--0.99814343 -- 0.46101272-- (-0.50636564)---- (-.9987636)

Calculate the value of f'(0.0099) to two place of accuracy.

3.

Let f(x) = 2/(x-8)

According to the definition of derivative, f'(x)= lim t-->x (2(x-8)-2(t-8))/((t-x)(t-8)(x-8))

The expression inside the limit simplifies to: 2/[-(x-8)/(t-8)]

Taking the limit of this fractional expression gives us

f′(x)= ?

Please, please, please help me. I am SO frustrated.

Thanks!