Functions in Algebra Examples

${\displaystyle V=\ln \left[\ln (3x-1)\right]}$
Find ${\displaystyle \frac{dV}{dx}}$

For the expression: $y=4x–2$, complete the following table: $\begin{array}{|ccccc|}\hline X:& 1& 3& 6& 10\\ Y:& \\ \hline\end{array}$

Look at this table: 

$\begin{array}{|cc|}\hline x& y\\ 1& 2\\ 2& 4\\ 3& 8\\ 4& 16\\ 5& 32\\ \hline\end{array}$

Write a linear $(y=mx+b),$ quadratic $(y=ax2)$, or exponential $(y=a(b)x)$ function that models the data.

$y=?$

Determine whether the sequence ${\displaystyle \left\{an\right\}\mathrm{\infty }}$
$n=2$ with ${\displaystyle an=\frac{\ln }{n}n2}$ converges.

Show all steps.

The circle whose equation is ${\displaystyle x²+y²=625}$ is where the point E(-7, 24) is located. What is the sine of an angle when it is drawn in standard position and its terminal ray passes through E? . 
(1) -7
(2) $-\frac{7}{24}$
(3) -24
(4) $-\frac{24}{25}$

to solve $\sin 2\theta -\cos \theta =0$

Which is

$\frac{1}{{\cos }^2\theta }$ simplified?

A. ${\sin }^2\theta$

B. ${\sec }^2\theta$

C. ${\csc }^2\theta$

D. ${\cot }^2\theta$

For $f(x)={\log }_{2}x$ between which two integers does f(40) lie? Explain.

Find the derivative of $cos³2x.(A)-sin³2x(B)-6cos²2x(C)6cos²2xsin2x(D)-3cos²2xsin2x(E)-6cos²2xsin2x$

How can modifications to the parameters affect how the graphs of exponential functions are translated?

For a certain product, the revenue is given by $R=40$: and the cost is given by $C=20x+1600$. To obtain a profit, the revenue must be greater than the cost. For what values of x will there be a profit?

$(2\sin \alpha +3\cos \alpha {)}^2+(3\sin \alpha -2\cos \alpha {)}^2=13$