Task MVT and L'Hopital's Rule

Evaluate the limit.

$$\lim_{x\rightarrow2}\ \frac{x^3-8}{x^2-4}$$  

Evaluate the limit.
$$\lim_{x\rightarrow2}\ \frac{x^2-4x+4}{x^3-12x+16}$$  

Find the value of c that satisfies the Mean Value Theorem over the given interval for $$f\left(x\right)=x^2;\ \ \left[1,3\right]$$  

Find the value of c that satisfies the Mean Value Theorem over the given interval for $$f\left(x\right)=\frac{x}{1+x};\ \ \left[1,3\right]$$  

Find the value of c that satisfies the Mean Value Theorem over the given interval for $$f\left(x\right)=\frac{x-2}{x-1};\ \ \left[0,2\right]$$  

Select ALL the equations for which the Mean Value Theorem DOES NOT APPLY

Find the value of c that satisfies the Mean Value Theorem over the given interval for $$f\left(x\right)=x^3+1;\ \ \left[-1,1\right]$$