Find the derivative of $f(x)=\sin \left(-8x+8\right)$, with $x$ in radians.

Evaluate ${\lim }_{x\to 0}\frac{\sin \left(3x\right)}{6x}$, with $x$ in radians.

Find the derivative of $w(x)=-3x^3+8x^2+7x-2$.

Let $u(x)=\{\begin{array}{ll}2x-9& x<-3\\ x^2+9& x\ge -3\end{array}$. Evaluate ${\lim }_{x\to -3^{-}}u(x)$.

Find the derivative of $r(x)=9x^9-7x$.

Find the area of the region enclosed by $y=-3x-2$ and $y=x^2$.

Approximate ${\int }_3^{6}3x^{2}dx$ with the TRAPEZOIDAL rule using $3$ equal subintervals.

Evaluate ${\int }_2^5\left(-7x+6\right)dx$.

Find the derivative of $u(x)={\left(5x^2-2\right)}^4$.

Find every critical point of $g(x)=2x^3-15x^2+36x$.

Find the average rate of change of $p(x)=-3x^2+2x+4$ on the interval $\left[4,7\right]$.

On which set is $q(x)=2x^3+12x^2+18x$ CONCAVE UP?

Evaluate ${\int }_0^{1}x{\left(x^2+4\right)}^{3}dx$.

Evaluate ${\lim }_{x\to \infty }\frac{-9x^2-7x}{-2x^2-7}$.

Find the equation of the line tangent to $f(x)=-x^2+2x$ at $x=2$.

For $\int x{\left(x^2+5\right)}^{6}dx$, which substitution turns the integral into one in $u$ alone?

For $s(x)=2x^3+21x^2+72x$, use the Second Derivative Test to classify the critical point at $x=-3$.

Evaluate ${\int }_0^{\frac{\pi }{3}}\sin xdx$, with $x$ in radians.

Find the area of the region bounded by $y=2x^2+3$, the $x$-axis, $x=2$ and $x=4$.

Find the second derivative of $w(x)=3x^3-x^2+3x+7$.

Find the absolute MAXIMUM VALUE of $w(x)=2x^3-6x^2-18x$ on $\left[-5,4\right]$.

Find the derivative of $f(x)=5x^{-5}$.

The Mean Value Theorem for Integrals is applied to $f(x)=e^x$ on $\left[0,2\right]$. Which hypothesis does the theorem require?

A particle has position $s(t)=2t^3+6t^2$ at time $t$. Is it speeding up or slowing down at $t=3$?

Each edge of a heated cube grows at $2$ centimeters per second. Its volume is $V=s^3$, where $s$ is the edge length. How fast is the volume changing when $s=4$ centimeters? Give the answer in cubic centimeters per second.

Is $y=7e^{4x}$ a solution of $\frac{dy}{dx}=3y$?

Find the derivative of $u(x)=\ln \left(4x+1\right)$, on an interval where the argument is positive.

If $q(x)={\int }_0^{\sqrt{x}}\cos \left(t^2\right)dt$, find $q^{\prime }\left(x\right)$.

Evaluate ${\lim }_{x\to 7}\frac{x^2-13x+42}{x^2-5x-14}$.

Use the definition $v^{\prime }(x)={\lim }_{h\to 0}\frac{v(x+h)-v(x)}{h}$ to find $v^{\prime }(x)$ for $v(x)=x^2+8x+9$.

Find the equation of the line normal to $r(x)=4x^2-4x$ at the point $\left(-5,120\right)$.

On which set is $s(x)=2x^3+3x^2-72x$ DECREASING?

Find $\frac{dy}{dx}$ for the relation $5x^2-3y^2=7$.

A radioactive sample decays continuously with a half-life of $3$ years. What is $k$ in $y=y_0{e}^{kt}$, with $t$ in years?

Evaluate ${\lim }_{x\to -5}\frac{x^2+9x+20}{x^2-x-30}$ using L'Hôpital's Rule.

Find the value of $c$ the Mean Value Theorem guarantees for $u(x)=x^2+8x$ on $\left[1,7\right]$.

Solve $\frac{dy}{dx}=4xy$ with $y(0)=7$, giving $y$ explicitly.

What is the average value of $f(x)=x^2+5$ on $\left[2,7\right]$?

The region bounded by $y=3x$, the $x$-axis, $x=0$ and $x=5$ is revolved about the $x$-axis. What is the volume?

Find the derivative of $u(x)=e^{6x^2-2}$.

If $q(x)={\int }_3^x\ln \left(t^2+1\right)dt$, find $q^{\prime }\left(x\right)$.

Evaluate ${\lim }_{x\to \infty }\frac{-x-6}{x^2-8}$.

Find $\int x\sqrt{x^2+5}dx$.

Find the derivative of $u(x)=3x^{5/3}$.

Evaluate $\int -8\sqrt[3]{x^7}dx$.

Find the derivative of $w(x)=\frac{3x-6}{3x+2}$.

Find the derivative of $w(x)=\sqrt{-4x^4+8}$.

Find the derivative of $u(x)=\left(3x^2+7\right)\left(-2x-4\right)$.

Let $p(x)=\{\begin{array}{ll}4x-3& x\le 4\\ 5x-7& x>4\end{array}$. Which statement about ${\lim }_{x\to 4}p(x)$ is correct?

Classify every critical point of $f(x)=2x^3-21x^2+72x$.

A circular ripple spreads so that its radius grows at $5$ centimeters per second, with $A=\pi r^2$. How fast is the area changing when the radius is $9$ centimeters? Give the answer in square centimeters per second.

Use the definition $r^{\prime }(x)={\lim }_{h\to 0}\frac{r(x+h)-r(x)}{h}$ to find $r^{\prime }(x)$ for $r(x)=-5x^2-2x-6$.

Evaluate ${\lim }_{x\to \infty }\frac{-4x+4}{x^2+2}$.

Find the derivative of $s(x)=e^{x^3-7}$.

Find the absolute MAXIMUM VALUE of $p(x)=2x^3+3x^2$ on $\left[-5,2\right]$.

Find the area of the region bounded by $y=x^3$, the $x$-axis, $x=1$ and $x=6$.

Evaluate $\int \left(-3x^8-9\right)dx$.

Find $\frac{dy}{dx}$ for the relation $-3x^2+7y^2=-4$.

Find the equation of the line normal to $f(x)=-2x^2+3x$ at the point $\left(-6,-90\right)$.

Find the value of $c$ the Mean Value Theorem guarantees for $r(x)=x^2+6x$ on $\left[-6,4\right]$.