Solve each equation. If the equation is an identity or if it has no solution, write identity or no solution. $3(2 t-6)=2(3 t-9)$

Find the solution of the given differential equation satisfying the stated conditions (express your answer implicitly if necessary). $\frac{d y}{d x}=\cos x, y(0)=1$.

What is a trigonometric identity?

Use Definition 2.4 .4 or 2.4 .5 to prove that the stated limit is correct.

$$\lim _{x \rightarrow 1} \frac{1}{|x-1|}=+\infty$$

Verify the identity.

$$\cos ( - x ) - \sin ( - x ) = \cos x + \sin x$$

Use a calculator or computer program to enter the annual highest temperature of record and the annual lowest temperature of record of selected cities found in Appendix discussed earlier.

Would you predict a linear relationship between the lowest and highest temperatures in a city? What value of the correlation coefficent $r$ would you predict?

Identify the computer fraud and abuse technique used in each of the following actual examples of computer wrongdoing.

t. It took Facebook 15 hours to kill a Facebook application that infected millions of PCs with software that displays a constant stream of pop-up ads. The program posted a “Sexiest Video Ever” message on Facebook walls that looked like it came from a friend. Clicking the link led to a Facebook installation screen, where users allowed the software to access their profiles and walls. Once approved, the application told users to download an updated, free version of a popular Windows video player. Instead, it inserted a program that displayed pop-up ads and links. A week later a “Distracting Beach Babes” message did the same thing.

The initial processing department had a beginning inventory of 750 units and an ending inventory of 1,350 units, and it started 9,500 units into production. How many were transferred out to the next department? A. 750 B. 1,350 C. 8,900 D. 10,250

Consider the equation

$$\frac{1+\tan x}{\sec x}=\sin x+\cos x$$

a) Verify graphically that the equation could be an identity. b) Prove that the equation is an identity for all permissible values of x.

Verify each identity. Give the domain of validity for each identity. ((sec θ)/(csc θ)) = tan θ

Find the amplitude of the oscillation $y-3 \sin 2 t+$ $4 \cos x 2 t$.

Find the curvature of the curve at the stated point. r(t)=2 cos ti+3 sin tj-tk;

$$t = \pi / 2$$

;

Solve each of the quadratic functions below by plotting a graph for the ranges of x stated. $-2 x^{2}+4 x-2=0 \ -2 \leqslant x \leqslant 4$

Design a CE amplifier with a resistance $R_{e}$ in the emitter to meet the following specifications: (i) Input resistance $R_{\mathrm{in}}=15 \mathrm{k} \Omega.$ (ii) When fed from a signal source with a peak amplitude of 0.15 V and a source resistance of $30 \mathrm{k} \Omega,$ the peak amplitude of $v_{\pi}$ is 5 mV. Specify $R_{e}$ and the bias current $I_{C}.$ The BJT has $\beta=74.$ If the total resistance in the collector is $6 \mathrm{k} \Omega,$ find the overall voltage gain $G_{v}$ and the peak amplitude of the output signal $v_{o}.$