Determine the following limits.
lim x→∞ (2x − 3) / (4x + 10)

The height above the ground of a stone thrown upwards is given by s(t), where t is measured in seconds. After 1 second, the height of the stone is 48 feet above the ground, and after 1.5 seconds, the height of the stone is 60 feet above the ground. Evaluate s(1) and s(1.5), and then find the average velocity of the stone over the time interval [1, 1.5].

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.

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

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

Find the intervals on which the following functions are continuous. Specify right- or left-continuity at the finite endpoints.

$g\left(x\right)=\cos \left(e^x\right)$

Use the graph of $f$ in the figure to determine the values of $x$ in the interval $(-3,5)$ at which f fails to be continuous. Justify your answers using the continuity checklist.

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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 $x=1$.