Suppose the rental cost for a snowboard is \$25 for the first day (or any part of the first day) plus \$15 for each additional day (or any part of a day).
e. For what values of t is f continuous? Explain.

For any real number x, the floor function (or greatest integer function) ⌊x⌋ is the greatest integer less than or equal to x (see figure).

a. Compute lim x→−1^− ⌊x⌋, lim x→−1^+ ⌊x⌋,lim x→2^− ⌊x⌋, and lim x→2^+ ⌊x⌋.

b. Estimate a solution to the equation in the given interval using a root finder.

x=cos x; (0,π/2)

Evaluate ${\(\displaystyle\[\lim\)_{x\(\to\]\infty\)}{f(x)}}$ and${\(\displaystyle\]\lim\)_{x\(\to\)-\(\infty\)}{f(x)}}$.

$f\left(x\right)=1-e^{-2x}$

Determine whether the following statements are true and give an explanation or counterexample.

a. The graph of a function can never cross one of its horizontal asymptotes.

Let $g\(\left\)(x\(\right\))=\(\frac{x^3-4x}{8\left|x-2\right|}\)$. <IMAGE>

Calculate $g\(\left\)(x\(\right\))$ for each value of $x$ in the following table.

Let $g\(\left\)(x\(\right\))=\(\begin{cases}\)5x-2 & \(\text{if }\)x<1\\ a & \(\text{if }\)x=1\\ ax^2+bx & \(\text{if }\)x>1\(\end{cases}\)$.

Determine values of the constants $a$ and $b$ , if possible, for which $g$ is continuous at $x=1$.