Homework 0

Homework 0 is due on 2/3/2023. Please try to submit the assignment as 1 PDF if possible.

Problem 1

Take a selfie at the different office hours locations. You will need 3 images.

Problem 2

Take a selfie with another professor at CSUCI.

Problem 3

Take a selfie at the Learning Resource Center (LRC). Identify any tutors that can help you with Math 352

Problem 4

Set the equation to 0 and solve for $x$:

1. $\ln(x^2+5)$
2. $x^2+6x+7$
3. $3x^2-5x+2$
4. $e^{x^2-4}$
5. $\ln(5x) + 3$

Problem 5

Complete the following derivatives:

1. $f(x)=e^x$

2. $f(x) = e^{x^2}$

3. $f(x) = e^x x^2$

4. $f(x) = \frac{\ln(x^2)}{x^2+3x}$

5. $f(x) = \ln(x)$

Problem 6

Complete the following integrals:

1. $\int-\frac{9}{x^4}dx$
2. $\int x^2\ln(x) dx$
3. $\int x^2\sqrt x dx$
4. $\int x^2e^{-x^3}dx$
5. $\int2x(x^2+1)^4dx$

Problem 7

Evaluate the following identities¹:

1. $(x+y)^n$
2. $\sum^\infty_{i=1}r^i$; $|r|<1$
   
3. $\sum^{m}_{i=1}r^i$; $|r|<1$
4. $\sum^\infty_{i=0}\frac{x^i}{i!}$
5. $\frac{n!}{(n-1)!}$

Footnotes

1. Either convert to summation notation or evaluate the summation.