A prompt says: "Use Euler's method with step size $1$, starting at $\left(4,2\right)$, to approximate $y$ at $x=7$." What does the prompt call for?

A particle has position $s(t)$. A prompt asks: "What is the average velocity of the particle on $\left[2,8\right]$?" What does the prompt call for?

A prompt asks: "What is the average value of $f$ on $\left[2,10\right]$?" What does the prompt call for?

A prompt asks, for $1\le x\le 6$: "Justify that this critical point of $f$ is a relative maximum." What does the prompt call for?

Fuel burned by an engine is measured at rate $F(t)$ liters per hour. A prompt asks: "How many liters in total over the first $12$ hours?" What does the prompt call for?

Let $M(t)$ be the mass of a decaying sample at time $t$ minutes. A prompt asks: "At what rate is the mass of a decaying sample changing at $t=5$ minutes?" What does the prompt call for?

Let $M(t)$ be the mass of a decaying sample at time $t$ minutes. A prompt asks: "At what rate is the mass of a decaying sample changing at $t=6$ minutes?" What does the prompt call for?

The flow of cars passing a checkpoint is measured at rate $C(t)$ cars per minute. A prompt asks: "How many cars in total over the first $10$ minutes?" What does the prompt call for?

A prompt asks, for $0\le t\le 8$: "at what times does the particle change direction?" What does the prompt call for?

Let $S(t)$ be the number of subscribers to a service at time $t$ weeks. A prompt asks: "At what rate is the number of subscribers to a service changing at $t=8$ weeks?" What does the prompt call for?

A prompt says: "The region between $y=f(x)$ and $y=g(x)$ from $x=2$ to $x=10$, with $f(x)\ge g(x)\ge 0$, is rotated about the $x$-axis." What does the prompt call for?

A prompt asks, for $1\le t\le 6$: "at what times does the particle change direction?" What does the prompt call for?

A prompt says: "$f$ is continuous on the closed interval $\left[2,6\right]$. Explain why $f$ must attain both a maximum and a minimum value on that interval." What does the prompt call for?

A prompt says: "$f$ is continuous on $\left[4,9\right]$ with $f(4)=-3$ and $f(9)=4$. Must there be a $c$ in $\left(4,9\right)$ with $f(c)=0$?" What does the prompt call for?

A prompt asks, for $0\le t\le 8$: "on what intervals is the graph of $f$ concave down?" What does the prompt call for?

A prompt says: "Use Euler's method with step size $1$, starting at $\left(4,4\right)$, to approximate $y$ at $x=7$." What does the prompt call for?

Let $W(t)$ be the number of gallons of water in a tank at time $t$ hours. A prompt asks: "At what rate is the number of gallons of water in a tank changing at $t=6$ hours?" What does the prompt call for?

Let $M(t)$ be the mass of a decaying sample at time $t$ minutes. A prompt asks: "At what rate is the mass of a decaying sample changing at $t=2$ minutes?" What does the prompt call for?

A leak draining a reservoir is measured at rate $L(t)$ gallons per hour. A prompt asks: "How many gallons in total over the first $9$ hours?" What does the prompt call for?

A prompt says: "$f$ is continuous on $\left[5,7\right]$, differentiable on $\left(5,7\right)$, and $f(5)=f(7)=5$. Must there be a $c$ with $f^{\prime }(c)=0$?" What does the prompt call for?

A prompt asks, for $1\le t\le 6$: "on what intervals is the particle speeding up?" What does the prompt call for?

A prompt asks: "What is the average value of $f$ on $\left[6,8\right]$?" What does the prompt call for?

A prompt says: "Region $R$ is bounded above by $y=f(x)$ and below by $y=g(x)$ from $x=1$ to $x=8$, and is the base of a solid whose cross sections perpendicular to the $x$-axis are squares." What does the prompt call for?

A prompt says: "$f$ is continuous on $\left[2,9\right]$ with $f(2)=-5$ and $f(9)=1$. Must there be a $c$ in $\left(2,9\right)$ with $f(c)=0$?" What does the prompt call for?

A prompt says: "Use Euler's method with step size $1$, starting at $\left(3,2\right)$, to approximate $y$ at $x=8$." What does the prompt call for?

A prompt says: "Region $R$ is bounded above by $y=f(x)$ and below by $y=g(x)$ from $x=4$ to $x=10$, and is the base of a solid whose cross sections perpendicular to the $x$-axis are squares." What does the prompt call for?

A table gives values of $f$ at $t=0,4,6,10$. A prompt asks: "Use a right Riemann sum with the three subintervals indicated by the table to approximate ${\int }_0^{10}f(t)dt$." What does the prompt call for?

Water entering a tank is measured at rate $R(t)$ gallons per hour. A prompt asks: "How many gallons in total over the first $10$ hours?" What does the prompt call for?

Fuel burned by an engine is measured at rate $F(t)$ liters per hour. A prompt asks: "How many liters in total over the first $11$ hours?" What does the prompt call for?

A particle has position $s(t)$. A prompt asks: "What is the average velocity of the particle on $\left[6,9\right]$?" What does the prompt call for?