Calculate the integral

Let . Calculate

Find the area of the largest rectangle that can be inscribed in a circle of radius .

Note: This type of question is called Hybrid. In the final exam there will be no uploading options until you have finished the exam. Once you submit the exam, a QR-code will be promoted in the screen; proceed to scan the QR-code with your mobile, and then proceed to take pictures of your hybrid questions, and upload them. 

Please be aware of this difference between the mock exam and the actual final exam. 

The derivative of is

Suppose a function has only two critical numbers, and , and . Which of the following statements are true?

1. has a global maximum at .
2. has a local minimum at .
3. has a solution between and .

4. is increasing between and .

5. has a point of inflection between and .

Evaluate the limit 

The derivative of is

Let be a piecewise function defined by for and for . Determine all values of where is continuous.