Few problems involving limits and the intermediate value

[John45]

Directions for this first one say to evalulate the limit or infinite limit.If the limit does not exist explain why.

Question 1
\(\displaystyle \:\lim_{x \to \ 2}\frac{(x+2)}{(x^2-4x+4)} \;\text{For this I got -1 / (x-2) so I think it doesn't exist but im not sure}\)

Question 2
Verify that the intermediate value theorem applies to the indicated interval and find the value of c guaranteed by the theorem.
\(\displaystyle \:f(x)= x^2+4x-11} \:[0,3] f(c)=1\)

 

[Assassin315]

Number one should be infinity. The limit as x->2 from the left is infinity. The limit as x->2 from the right is infinity. Therefore, the limit as x->2 is infinity.

For number two, the IVT says that, provided f:IR -> IR and f is continuous, the function will take on every point between the bottom-most and top-most points. So, calculate what f(0), f(1) and f(3) are. Show f(0) < f(1) < f(3)?