Calculus 2 Equations: Expert Solutions and More

$\sum _{x=1}^{\mathrm{\infty }}\frac{n+6}{n^2+12n+8}$

$P(3,-4,-1)$ passing through point $v=i+j+k$.
Write the parametric equation of the line parallel to its vector

Find if the following first order differential equations seperable, linear, exact, almost exact, homogeneous, or Bernoulli. Rewrite the equation into standard form for the classification it fits.
${\displaystyle [\left(2\right)\left(x\right)\left(y^3\right)+1]dx=[\left(y^{-1}\right)-\left(3\right)\left(x^2\right)\left(y^2\right)]dy}$

Find if the following first order differential equations seperable, linear, exact, almost exact, homogeneous, or Bernoulli. Rewrite the equation into standard form for the classification it fits.
${\displaystyle -[y^4-\left(t\right)\left(y^3\right)]dt=\left(3\right)\left(t^2\right)\left(y^2\right)dy}$

Find polar equation for the circle. Sketch circle in the coordinate plane and label it with both its Cartesian and polar equations. ${\displaystyle x^2+2x+y^2=0}$

${\displaystyle r\left(t\right)=\left(\sin t\right)i+(1+\cos t)j+{\left(4t\right)}^{2}k}$ vector -valued fuction defined in the from is given.
${\displaystyle {\int }_0^{\frac{\pi }{2}}r\left(t\right)dt}$ calculate its integral

Find zw and ${\displaystyle \frac{z}{w}}$. Leave your answers in polar form.
${\displaystyle z=\cos 80°+i\sin 80°}$
${\displaystyle w=\cos 50°+i\sin 50°}$

The quadratic formula is used to solve for x in equations taking the form of a quadratic equation, ${\displaystyle a{x}^2+bc+c=0}$
solve for x in the expression using the quadratic formula.
${\displaystyle 2x^2+15x-9.1=0}$

In polar coordinates ${\displaystyle r^2=-6r\sin \theta }$ the equation in Cartesian coordinates find theb equation and plot it

Solve the system of equations with elimination method and what is the type of solution?
$\{\begin{array}{l}x–2y=-3\\ 4x-3y=10\end{array}$

Write an equation in the indicated coordinate system. Also write a parametric equation and a vector equation for the following equation
${\displaystyle x^2+y^2=100\in R^2}$, polar coordinates

Find a basis for the set of vectors in ${\displaystyle {\mathbb{R}}^3}$ in the plane $x-6y+9z=0$.[Hint: Think of the equation as a​ "system" of homogeneous​ equations.]
A basis for the set of vectors in ${\displaystyle {\mathbb{R}}^3}$ in the plane $x-6y+9z=0$

Write an equation in the indicated coordinate system. Also write a parametric equation and a vector equation for the following equation
${\displaystyle x^2+y^2=25\in R^3}$, cylindrical coordinates, sherical coordinates

Find all values of x such that the tangent line to ${\displaystyle f\left(x\right)={\left(x^2–9\right)}^2}$ is horizontal.

Consider the parametric equations:
${\displaystyle x=e^t}$
${\displaystyle y=3e^{-2t}}$
Find ${\displaystyle \frac{dy}{dx}}$ at the point $(1,3)$

Find all points (if any) of horizontal and vertical tangency to the curve:
${\displaystyle x=1-t.y=t^2}$

The Cartesian coordinates of a point are given.
(−9, 9)
(i) Find polar coordinates $(r,\theta )$ of the point, where r > 0
and ${\displaystyle 0\le \theta <2?.}$

Do the lines ${\displaystyle \frac{x}{3}=\frac{y}{2}=\frac{z}{2}\text{and}\frac{x}{5}=\frac{y}{3}=\frac{z-4}{2}}$ intersect?

Replace the Cartesian equation with equivalent polar equations. $x=y$

Convert the following coordinates between rectangular and polar form
${\displaystyle (-1,\sqrt{3})}$