Question

1. Explain why the function

f(x)=(x^2-4)/(x-2)
is not continous on [0,3]. what kind of discontinuity occurs?

2. use areas to show that

integral sign with the upper limit of 3 and a lower limit of 0 (x^2-4/x-2)dx=10.5

3. use the area to show that

intergral sign with the upper limit of 5 and a lower limit of 0 (int(x)dx)=10

Answer 1

Please try first, ask us when you are stuck.
You know that when a denominator is zero there is trouble.
Simplify by factoring or whatever the expression inside before integrating.
I get 25/2 for integral from 0 to 5 of x dx. Graph of y = x is a triangle. The altitude is 5 and the base is 5.