{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

sample_final

# sample_final - MAT16b Sample Final Problem 1(15 pts Find...

This preview shows pages 1–2. Sign up to view the full content.

MAT16b Sample Final Problem 1. (15 pts) Find the following indefinite integrals (antiderivatives): (a) Z x ln( x ) dx (b) Z ln( x ) x dx (c) Z 1 x ln 2 ( x ) dx Problem 2. (15 pts) Find the following definite integrals: (a) Z π/ 2 0 x cos( x ) dx (b) Z ln(2) 0 e x e x - 1 dx (c) Z π/ 2 0 sin( x ) cos( x ) dx Problem 3. (20 pts) Which of the following improper integrals converge and which diverge? (a) Z 0 t 2 e - t 3 dt (b) Z 2 1 1 ( t - 1) 2 dt (c) Z 1 0 1 t dt (d) Z 0 -∞ e - t dt (e) Z 1 - 1 1 1 - x 2 dt Problem 4. (10 pts) Find all of the critical points of the function f ( x ) = 2 sin( x ) in the interval [0 , 2 π ). 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Problem 5. (15 pts) Find the antiderivative of the function f ( x ) = x 2 - 1 x 2 + 2 x - 8 . Problem 6. (15 pts) Let X be a random variable with values in the interval [0 , ) whose probability density function is f ( x ) = e - x . What is the expected value of
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

sample_final - MAT16b Sample Final Problem 1(15 pts Find...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online