Maritza remembers her PIN because it is the product of two consecutive prime numbers that is between 1000 and 1500. What is her PIN?

For the following function, a. use the Equation to find the slope of the tangent line $m_{\tan }=f^{\prime}(a)$ and b. find the equation of the tangent line to f at x = a. $f(x)=\frac{7}{x}, a=3$

Without using any trigonometric identities, find

$$\lim _ { x \rightarrow 0 } \frac { \tan ( x + y ) - \tan y } { x }$$

[Hint: Relate the given limit to the definition of the derivative of an appropriate function of y.]

For the following function, a. use the Equation to find the slope of the tangent line $m_{\tan }=f^{\prime}(a)$ and b. find the equation of the tangent line to f at x = a. $f(x)=1-x-x^{2}, a=0$

Find the integral involving secant and tangent.

$$\displaystyle\int \sec ^2 x \tan x \ dx$$

Divide and, if possible, simplify.

$$\frac{-3+3 x}{16} \div \frac{x-1}{5}$$

Divide and, if possible, simplify.

$$\frac{x-1}{x+2} \div \frac{1-x}{4+x^2}$$

Suppose that 10% of the numbers in a list 15,20% of the numbers are 25, and the remaining numbers are 50. What is the average of the numbers in the list?

Solve given quadratic equation by factoring.

2x - 1 = -8 x raised to 2

What are the functions of aerial roots?​

Divide and simplify.

$$\frac{-12+4 x}{4} \div \frac{-6+2 x}{6}$$

Differentiate the following functions with respect to $x$.

$$y=\ln (f(x))$$

Divide and, if possible, simplify.

$$\frac{-4+2 x}{15} \div \frac{x-2}{3}$$

Divide and simplify.

$$\frac{-6+3 x}{5} \div \frac{4 x-8}{25}$$