Is the constant function $y\left(t\right)=-4$ a solution to the differential equation $y^{\prime }=t^2(y+4)$?

If $f\left(x\right)=2x^2+1$, what is the value of $f\left(3\right)$?

Given the sphere defined by the equation $x^2+y^2+z^2=9$, what is the intersection of this sphere with the yz-plane?

What is the area enclosed by the curves $y=x^3-8x^2+18x-5$ and $y=x+5$?

Consider the geometric series with first term $2$ and common ratio $\frac{1}{2}$. Write out the first four terms of the series: $2,1,\frac{1}{2},\frac{1}{4}$. What is the sum of the infinite series?

If $f\left(x\right)=x^2$, which of the following is the value of $f(-3)$?

If $f\left(x\right)=x^3$, which of the following is the value of $f(-2)$?

Given the function $f\left(x\right)=x^2$ defined on the interval $0\le x\le 2$, determine the y-coordinate of the centroid of the region bounded by the graph of $f\left(x\right)$, the x-axis, and the lines $x=0$ and $x=2$.

Let $g\left(x\right)={\int }_0^{x}f\left(t\right)dt$, where $f$ is the function whose graph is shown. Which of the following statements is true about $g\left(x\right)$?