Explain how you can you tell whether a function of the form f(x) = ax² has a minimum or a maximum value and what that value is.

Find the limits.

$f(x)=5-x$, $g(x)=x^3$ $\quad$ (b) $\lim_{x\to 4}g(x)$

Let X and Y be two independent uniforms (0,1) random variables. Let M be the smaller of $X$ and $Y$. Let $0<x<1$.

a) Represent the event $(M \geq x)$ as the region in the plane, and find $P(M \geq x)$ as the area of this region.

b) Use your result in a) to find the c.d.f. and density of $M$. Sketch the graph of these functions.

Explain how you can tell whether a quadratic function has a maximum value or a minimum value without graphing the function.

Evaluate the limits that exist.
$\lim\limits_{x \to 0} \frac{2x}{\sin x}$.

Find the limits for the given expression.

$$\lim _{t \rightarrow \pi / 2^{+}} e^{\tan t}$$

Evaluate the limits that exist.
$\lim\limits_{x \to -4}\left(x^2+3x-7\right)$.

Sketch the function $f(x)=x^3-3 x+1$.

Repeat steps 1-6 for $y=-f(x)$. A point where the graph of a function is continuous and where the concavity changes is a point of inflexion.

What is the lambda max value?

Define genocide, ethnic cleansing.

State the hypothesis and the conclusion of the statement.

All squares are rectangles.

Evaluate the following limits.

$$\lim _{x \rightarrow 2} \frac{x^3-8}{x^2-4}$$

Find the limits.

$$\lim _ { y \rightarrow 4 } \frac { 4 - y } { 2 - \sqrt { y } }$$

Find the limit (if it exists). If the limit does not exist, explain why. Use a graphing utility to verify your result graphically.

$$\lim _{x \rightarrow 4}\left(5 x-x^2\right)$$