My homework is due really soon.(adsbygoogle = window.adsbygoogle || []).push({});

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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# How to find f'(0) from a left handed limit? (multiple questions)

**Physics Forums | Science Articles, Homework Help, Discussion**