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1.  If \(f(x) = x^2\sin(2x)\), then \(f'(x)\) equals

a.  \(2x\cos(2x)\)

b.  \(4x\cos(2x)\)

c.  \(x^2\cos(2x)+2x\sin(2x)\)

d.  \(2x^2\cos(2x)+2x\sin(2x)\)

e.  \(x^2\sin(2x)+2x\cos(2x)\)

2.  Integrate \(\int e^{2x}dx\).

a.  \(e^{x^2}+c\)

b.  \(e^{2x+1}+c\)

c.  \(2e^{2x}+c\)

d.  \(e^{2x}+c\)

e.  \(\frac{1}{2}e^{2x}+c\)

3.  Integrate\(\int \sin^4x \cos x dx\)

a.  \(\frac{1}{5} \cos^5 x \frac{1}{2}\sin^2 x + c\)

b.  \(\frac{1}{5} \cos^5 x + c\)

c.  \(\frac{1}{5} \sin^5 x + c\)

d.  \(\frac{1}{5} \sin^5 x \frac{1}{2}\cos^2 x + c\)

e.  \(\cos^5 x \sin^2 x + c\)

4.  Integrate\(\int x 2^x dx\)

a.  \(\frac{x}{x+1}2^{x+1}+ c\)

b.  \(\frac{1}{\ln 2}x 2^x - \frac{1}{(\ln 2)^2} 2^x + c\)

c.  \(x 2^x - \frac{1}{\ln 2} 2^x + c\)

d.  \(\frac{1}{(\ln 2)^2}x 2^x - \frac{1}{(\ln 2)^3} 2^x + c\)

e.  \(\frac{1}{x+1}2^{x+1} + c\)

5.  To be written out and submitted on Monday, Jan. 27: Determine whether or not \(y(t) = \frac{1}{t}\) is a solution to the differential equation \(2t^2 y''+3ty' = y\). Show all steps in your work. And, as usual, when verifying equations, don't write any equal signs that you can't justify. Instead, work out the left side and the right side separately to see whether or not they are equal.