Use the $\epsilon=\delta$ definition of limit to verify the limit statements given.

$$\lim _{(x, y) \rightarrow(0,0)}\left(x+y^{2}\right)=0$$

How many different 5-card hands can be obtained from a deck of 52 cards?

State the formal definition of a limit.

Use the $\epsilon=\delta$ definition of limit to verify the limit statements given.

$$\lim _{(x, y) \rightarrow(0,0)}\left(2 x^{2}+3 y^{2}\right)=0$$

In the following exercise, find the value(s) of k that makes the function continuous over the given interval.

$$f(x)=\left\{\begin{array}{cl} e^{k x}, & 0 \leq x<4 \\ x+3, & 4 \leq x \leq 8 \end{array}\right.$$

In the following exercise, find the value(s) of k that makes the function continuous over the given interval.

$$f(x)=\left\{\begin{aligned} \frac{x^{2}+3 x+2}{x+2}, & x \neq-2 \\ k, & x=-2 \end{aligned}\right.$$

Evaluating Which do you think have a greater influence on a teen's thoughts about smoking-tobacco ads or anti-tobacco ads?

Answer for the sequence $x$ defined by $x_1=2$, $x_n=3+x_{n-1}$, $n\geq 2$. Is $x$ nondecreasing?

Find the equation in standard form for the line that satisfies the given requirements. -horizontal line through (-2, -5)

For the following exercise, decide if the function continuous at the given point. If it is discontinuous, what type of discontinuity is it? $f(y)=\frac{\sin (\pi y)}{\tan (\pi y)}, \text { at } y=1$

Decide whether the function is continuous on the given interval. If not, define or redefine the function at one point to make it continuous everywhere on the given interval, or else explain why that cannot be done.

$$f(x)=\frac{x+4}{x-8} \text { on }[0,10]$$

Find the exact value of each quadrantal angle. If any are not defined, write undefined. $\csc 1080 ^ { \circ }$

Find a function y=f(x) that describes the parametric curve x=-2t+1, y=

$$3t^2$$

, for

$$- \infty < t < \infty$$

.

For the following exercise, determine the point(s), if any, at which the function is discontinuous. Classify any discontinuity as jump, removable, infinite, or other. $f(x)=\frac{x}{x^{2}-x}$