Help to Integral Calculus Solutions & Examples

A ball is dropped from the top of a tall building. If air resistance is taken into account, recall that the downward velocity v of the ball is modeled by the differential equation:
$dv/dt=g-<!--\; -\; -->pv$
where g = 9.8 $m/se{c}^2$ is the acceleration due to gravity, and p = 0.1 is the drag coefficient. Assuming the initial velocity of the ball is zero, use Euler’s method with a step size of h = .25 sec to estimate the velocity of the ball after one second. Keep track of three decimal places during the calculation.

I just started learning the Euler's method. Can someone help me with this problem. I know that:
$dv/dt=f(v,t)=g-<!--\; -\; -->pv$
I plug the numbers given into the equation: $dv/dt=9.8-<!--\; -\; -->.25v$
change of x = step size (h) = .25
I think $(v(0),t(0))=(0,0)$??

Convert the polar equation to a rectangular equation.
$r=-<!--\; -\; -->9\cos <!--\; \; -->\mathrm{\theta <!--\; \theta \; -->}$

Write in simplified radical form: $\sqrt[3]{128}=$
$\sqrt[5]{96x^{20}{y}^{11}}$

Determine convergence / divergence of $\sum <!--\; \sum \; -->\sin <!--\; \; -->\frac{\mathrm{\pi <!--\; \pi \; -->}}{n^2}$.
Let $a_n=\sin <!--\; \; -->\frac{\mathrm{\pi <!--\; \pi \; -->}}{n^2}$.
I attempted the integral test but on the interval $[1,\sqrt{2})$ it is increasing and decreasing on $(\sqrt{2},\mathrm{\infty <!--\; \infty \; -->})$. So the integral test in only applicable for the decreasing part. + the integral computation seems to lead to 3 pages of steps...
I believe the comparison test would be the most reasonable test, graphically I observed that $a_n$ behaves like $b_n=1/n$ when n is large.
$\sum <!--\; \sum \; -->b_n=\mathrm{\infty <!--\; \infty \; -->}$; but, since $b_n>a_n⟹<!--\; ⟹\; -->$ inconclusive for divergence/convergence.
I attempted the limit comparison, and ratio test, but inconclusive. I am uncertain if I am doing them properly.
How could I bound below $a_n$ to proceed with the comparison test? Is there a more appropriate method? How would you proceed?

Find the corresponding rectangular equation represented by the parameteric equations; $x=1+\sec <!--\; \; -->\mathrm{\theta <!--\; \theta \; -->}andy=2+\tan <!--\; \; -->\mathrm{\theta <!--\; \theta \; -->}$ by eliminating the parameter.

Rewrite with rational exponents.
$(\sqrt[13]{7x^{2}y}{)}^3$

find the indefinite integral.
Integral of 2t-1/t squared - t + 2 dt

Find an equation for each sphere that passes through the point(5,1,4) and is tangent to all three coordinate planes.

at room temperature, glass used in windows actually has some properties in a liquid. it has a very slow, viscious flow glass does not become a true liquid until temperatures are greater than or equal to 525 degreesC. Find the Farenheit temperatures for which glass is a liquid
Formula is F = 9/5 C + 32
= {F/F less than or equal to ?}

Find parametric equations and symmetric equation for the line through (-2,2,3) which is parallel to x + 1 = (y/3) = z - 2.

Sketch the region whose signed area is represented by the definite integral, and evaluate the integral using an appropriate formula from geomety, where needed.
${\int <!--\; \int \; -->}_{-<!--\; -\; -->1}^2|2x-<!--\; -\; -->3|dx$

Find the parametric equation for the line through (5,1,0) that is perpendicular to the plane 2x - y + z = 1.

Convert the rectangular equation to polar form.
$x^2+y^2-<!--\; -\; -->4ax=0$
r=?

Use integration by parts to prove the reduction formula.
$\int <!--\; \int \; -->x^n{e}^{x}dx=x^n{e}^x-<!--\; -\; -->n\int <!--\; \int \; -->x^{n-<!--\; -\; -->1}{e}^{x}dx$

Find the parametric equations for the line segment from P to Q. (0 less than or equal to t less than or equal to 1)
P=(11,3,2), Q=(9,6,-1)

a) Does the relation "is less than" have a transitive property?
b)$\mathrm{\angle <!--\; \angle \; -->}$3 is acute while $\mathrm{\angle <!--\; \angle \; -->}$4 is obtuse. State an inequality involving the measure of $\mathrm{\angle <!--\; \angle \; -->}$3 and $\mathrm{\angle <!--\; \angle \; -->}$4.
c) Where points M and N are midpoints of AB and CD, respectively it is given that AM $\cong <!--\; \cong \; -->$ CN... State a conclusion regarding AB and CD.