Homework 0

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Problem 1

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 2

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 3

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 4

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.