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?

Average single-family home prices P (in thousands of dollars) in Sacramento, California, are shown in the accompanying figure from the beginning of 2006 through the end of 2015.

b. Estimate home prices at the end of

i) 2007 ii) 2012 iii) 2015

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 $y=x+5$?

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

If $f\left(x\right)=x^2$, 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 $x=2$.