# Calculus 2 questions and answers

Recent questions in Calculus 2
Applications of integrals

### Calicillian is Available as 125 mg tablet how many tablets are messed to give a dose of 375 mg

Differential equations

### Find transient terms in this general solution to a differential equation, if there are any $$\displaystyle{y}={\left({x}+{C}\right)}{\left({\frac{{{x}+{2}}}{{{x}-{2}}}}\right)}$$

Differential equations

### 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. $$\displaystyle{\left({x}\right)}{\left({e}^{{y}}\right)}{\left(\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}\right)}={e}^{{-{2}{x}}}+{e}^{{{y}-{2}{x}}}$$

Parametric equations

### Sketch the vector field F by drawing a diagram. $$\displaystyle{F}{\left({x},{y}\right)}={\frac{{{y}{i}+{x}{j}}}{{{\left({x}^{{{2}}}+{y}^{{{2}}}\right)}^{{{\frac{{{1}}}{{{2}}}}}}}}}$$

Parametric equations

### Find the area of the region that lies inside both curves. $$\displaystyle{r}=\sqrt{{3}}{\cos{\theta}},{r}={\sin{\theta}}$$

Parametric equations

### Find sets of parametric equations and symmetric equations of the line that passes through the given point and is parallel to the given vector or line. (For each line, write the direction numbers as integers.) Point: (-3, 4, 5) Parallel to: $$\displaystyle\frac{{{x}-{1}}}{{2}}=\frac{{{y}+{1}}}{ -{{3}}}={z}-{5}$$ (a) Parametric equations (b) Symmetric equations

Parametric equations

### Replace the Cartesian equation with equivalent polar equations. x = 7

Parametric equations

### Given the points (2,6) and (6,10), find at least three equations from exponential function that pass through these point

Parametric equations

### For the given polar equation, write an equivalent rectangular equation $$\displaystyle{r}{\cos{\theta}}={13}$$

Parametric equations

### Replace the polar equations with equivalent Cartesian equations. Then describe or identify the graph. $$\displaystyle{r}^{{{2}}}=-{4}{r}{\cos{\theta}}$$

Parametric equations

### Convert the point from rectangular coordinates to spherical coordinates. $$\displaystyle{\left(-{3},-{3},\sqrt{{{2}}}\right)}$$

Parametric equations

Calculus 2

Calculus 2

### A quadratic function f is given (a)Express f in standard form (b)Find the vertex and x- and y-intercepts of f. (c)Sketch the graph. (d)Find the domain and range of f. $$\displaystyle{f{{\left({x}\right)}}}={x}^{{{2}}}-{2}{x}+{3}$$

Parametric equations

### Find the length of the parametric curve defined over the given interval $$\displaystyle{x}={3}{t}-{6},{y}={6}{t}+{1},{0}\le{t}\le{1}$$

Differential equations

### $$\displaystyle{\left(\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}\right)}=-\frac{{{y}^{{2}}+{x}^{{2}}}}{{{2}{x}{y}}}{\quad\text{and}\quad}{y}{\left({1}\right)}={4}$$ Please, solve the differential equation. Write the method you used and solve for the dependent variable it it is possible.

Differential equations

### 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. $$\displaystyle{\left(\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}\right)}={x}^{{2}}{\left[{\left({x}^{{3}}\right)}{\left({y}\right)}-{\left(\frac{{1}}{{x}}\right)}\right]}$$

Parametric equations

### A vector-valued function $$r(t)$$ with its defining parametric equations is given by the following. $$x = f(t)$$ $$y = g(t)$$ $$r(t) = ft(i) + g(t)j$$ Now find the vector-valued function $$r(t)$$ with the given parametric equations.

Parametric equations

### Polar coordinates of point P are given. Find all of its polar coordinates. $$\displaystyle{P}={\left({1},-\frac{\pi}{{4}}\right)}$$

Parametric equations