Test Your Knowledge 20120209

Look through and see if you can do these. Try to work them out. You may submit questions here and qualify for participation of Class Discussion due 20120214.

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Factor $x^2-2xy+y^2$.

What is the quadratic formula?

What are the addition and subtraction formulas for $\sin$ and $\cos$?
$\sin(x+y)=?$
$\sin(x-y)=?$
$\cos(x+y)=?$
$\cos(x-y)=?$

What is $\tan(0)$?

Compute $$\int s \cos (\alpha s) ds$$
Note that the integral is with respect to the variable $s$ and so $\alpha$ acts like a constant.
(See Example 7.1.1 and Problem 7.1.8)

Compute $$\int t e^t dt$$
(See Example 7.1.3)

Compute $$\int \cos(5 r) \cos(3r) dr$$
(See Example 7.2.9 and Problem 7.2.41-43)

Reference page 5, Inverse Trigonometric Functions:
$$\frac{d}{dx}(\sin^{-1}x)=\frac{1}{\sqrt{1-x^2}}$$
$$\frac{d}{dx}(\cos^{-1}x)=-\frac{1}{\sqrt{1-x^2}}$$
$$\frac{d}{dx}(\tan^{-1}x)=\frac{1}{1+x^2}$$