Determine the y-intercept and the end behavior of the following functions. $y=5 x^{12}+43 x^{8}-14 x^{5}+12 x^{2}+8 x$

Determine the end behavior of each function as $x \to +\infty$ and as $x \to −\infty$.

$$f(x)=5x^4 − 25x^3 − 62x^2 + 5x + 300$$

Graph y = tan x and y = cot x together for $-7 \leq x \leq 7.$ Comment on the behavior of cot x in relation to the signs and values of tan x.

Name three careers in today's world that might provide work for humorists. Justify how humor is used in each case.

Imagine that you are a barber in a world without money. Explain why it would be tricky to obtain groceries, clothing, and a place to live.

he General Social Survey, run annually, asked respondents "Do you have in your home (or garage) any guns or revolvers?" The replies are shown in the table. (sda.berkeley.edu/cgi-bin/hsda? harcsda+gss10)

Assume we select three adults at random from this sample.

c) What assumption did you make in computing these probabilities?

For each term or name below, write a sentence explaining its significance to World War II. 5. Final Solution

What does their calm detachment in the midst of describing chaotic events divulge about the writers' views of the world around them?

How do you think making real-world comparisons with cells helps you understand cell structure and function?

Describe four states of matter by using the terms solid, liquid, gos, and plasma. Describe the behavior of particles in each state.

The end behavior asymptote of the function f is one of the following. Which one is it? $y=-x^{3}$. $f(x)=\frac{x^{4}+2 x^{2}+x+1}{x-3}$

Computing the derivative of $f(x)=x^2 e^x$ (a). Use the definition of the derivative to show that $\frac{d}{d x}\left(x^2 e^x\right)=e^x \cdot \lim _{h \rightarrow 0} \frac{\left(x^2+2 x h+h^2\right) e^h-x^2}{h}$. (b). Manipulate the limit in part (a) to arrive at $f^{\prime}(x)=e^x\left(x^2+2 x\right) \cdot\left(\right.$ Hint $:$ Use the fact that $\lim _{h \rightarrow 0} \frac{e^h-1}{h}=1$.)

A(n) _______________ __________________ ___________ is a fixed flow of responses that occurs in reaction to a specific stimulus. The specific stimulus that elicits this behavior is called a s________ stimulus or re _____________.

The vector spaces N(A), R(A), N(Aᵀ), and R(Aᵀ) are the four fundamental subspaces associated with a matrix A. We can use MATLAB to construct orthonormal bases for each of the fundamental subspaces associated with a given matrix. We can then construct projection matrices corresponding to each subspace. Set A = rand(5, 2) ∗ rand(2, 5). What would you expect the rank and nullity of A to be? Explain. Use MATLAB to check your answer by computing rank(A) and Z = null(A). The columns of Z form an orthonormal basis for N(A).