Find each integral. $\int(3 \cos x-4 \sin x) d x$

The following programs or program segments has errors. Find as many as you can. char x = 'a', y = 'a'; if (strcmp(x, y) == 0) exit(0);

Decide whether each function defined as follows is a probability density function for the given interval. $f(x)=\sqrt{x}$; [4, 9]

Integrate the function $f (x, y) = x + y$ over the region bounded by $x + y = 2$ and $y^2 − 2y − x = 0.$

What types of energy make up the internal energy of monatomic gases? How about diatomic gases?

Write each expression in interval notation. Graph each interval. x<4

Solve each equation by factoring or by using the quadratic formula. If the solutions involve square roots, give both the exact solutions and the approximate solutions to three decimal places. $m^{2}=14 m-49$

Calculate the inverse Laplace transform of:

$$\begin{array}{ll}{\text { (a) } \frac{6(s-1)}{s^{4}-1}} & {\text { (b) } \frac{s e^{-\pi s}}{s^{2}+1}} \\ {\text { (c) } \frac{8}{s(s+1)^{3}}}\end{array}$$

Prove $\frac{d}{d x} \ln |a x|=\frac{d}{d x} \ln |x|$ for any constant a.

Find the general solution for each differential equation. Verify that each solution satisfies the original differential equation. $y \frac{d y}{d x}=x^{2}-x$

Find the domain and range of the function. Write your answer in interval notation. $g(x)=\sqrt{16-x^{4}}$

Find the derivative of each function. $y=-4 \sin 7 x$

Find F(s) if: (a) $f(t)=6 e^{-t} \cosh 2 t$ (b) $f(t)=3 t e^{-2 t} \sinh 4 t$ (c) $f(t)=8 e^{-3 t} \cosh t u(t-2)$

Use a counterexample to show that the statement is false. The product of two irrational numbers is irrational.