One variable calculus for non majors questions.

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#	Question
1	Evaluate the following integral $int_{0}^{infty } e^{-8x} dx$ Mathematical Calculation
2	What it means by saying that a function $f$ is periodic ? Is a function defined by $f(x)=cos sqrt{3x}$ periodic ? If yes , use the definition to determine its period. Mathematical Calculation
3	Solve the differential equation $3xfrac{dy}{dx}+y+x^2y^4=0$ Mathematical Calculation
4	Evaluate $lim_{n oinfty }sqrt[n]{n}$ where n=1,2,3….. Mathematical Calculation
5	If $lim_{n o infty }(1+frac{t}{n})^n=e^t$ , find $lim_{n o infty }(frac{n+12}{n})^{5n}$ Mathematical Calculation
6	Prove that $sum_{n=2}^{infty }frac{1}{n^2-1}$ converges, and find its sum. Mathematical Calculation
7	If the fourier series representation for the function $f(x)=left{egin{matrix} 0 & if&-pi< X<0 \ pi &if &0<X<pi end{matrix} ight.$ is $frac{pi}{2}+2(sinx+frac{sin3x}{3}+frac{sin5x}{5}+...).$ Use the results to find the fourier representation for $g(x)=left{egin{matrix} -frac{1}{pi} & if&-pi< X<0 \ frac{1}{pi} &if &0<X<pi end{matrix} ight.$ Mathematical Calculation
8	Apply the rule of False Position to compute $x_3$ for $x^3-2x-5=0$ given that $x_0=-1$ , $x_1=3.$ Mathematical Calculation
9	Find the cubic polynomial which takes the following values y(0)=1, y(1)=0, y(2)=1 and y(3)=10. Mathematical Calculation
10	Evaluate $int_{-3}^{4} left \| x+2 ight \|dx$ Mathematical Calculation