# High school calculus questions and answers

Recent questions in Calculus and Analysis
Matrices

### Hello everyone! I'm a college student and taking a couse of Electrical Engineering. I hope you will help me with my homework. Thank you! The bases of a trapezoid are 22 and 12 respectively. The angles at the extremities of one base are 65° and 40° respectively. Find the two legs.

Applications of integrals

Matrices

### If the roots of $$ax^{2}+bx+c=0$$ are $$\frac{3}{2},\frac{4}{3}$$ then $$(a+b+c)^{2} =$$

Calculus and Analysis

Derivatives

Derivatives

Derivatives

Derivatives

Derivatives

### Using the definition, calculate the derivatives of the functions. Then find the values of the derivatives as specified. $$\displaystyle{k}{\left({z}\right)}={\frac{{{1}-{z}}}{{{2}{z}}}};{k}'{\left(-{1}\right)},{k}'{\left({1}\right)},{k}'{\left(\sqrt{{{2}}}\right)}$$

Rational functions

### Graph the rational functions. $$y=\frac{(x^{3})+x-2)}{(x-(x^{2})}$$

Rational functions

### determine whether the statement is true or false. Justify your answer. When your attempt to find the limit of a rational function yields the indeterminate form 0/0, the rational function’s numerator and denominator have a common factor.

Polynomial graphs

### For the following exercise, for each polynomial, a. find the degree. b. find the zeros, if any. c. find the y-intercept(s), if any. d. use the leading coefficient to determine the graph’s end behavior. and e. determine algebraically whether the polynomial is even, odd, or neither. $$\displaystyle{f{{\left({x}\right)}}}=-{3}{x}^{{2}}+{6}{x}$$

Polynomial graphs

### For the following exercise, for each polynomial, a. find the degree. b. find the zeros, if any. c. find the y-intercept(s), if any. d. use the leading coefficient to determine the graph’s end behavior. and e. determine algebraically whether the polynomial is even, odd, or neither. $$\displaystyle{f{{\left({x}\right)}}}={3}{x}−{x}^{{3}}$$

Transformations of functions

### State the parent function that must be transformed to create the graph of each of the following functions. Then describe the transformations that must be applied to the parent function. a) $$\displaystyle{y}={\left(\frac{{5}}{{4}}\right)}{x}^{{4}}+{3}$$ b) $$y=3x-4$$ c) $$\displaystyle{y}={\left({3}{x}+{4}\right)}^{{3}}-{7}$$ d) $$\displaystyle{y}=-{\left({x}+{8}\right)}^{{4}}$$ e) $$y=-4.8(x-3)(x-3)$$ f) $$\displaystyle{2}{\left({\left(\frac{{1}}{{5}}\right)}{x}+{7}\right)}^{{3}}-{4}$$

Transformations of functions

### Find the limit (if it exists) and discuss the continuity of the function. $$\lim_{(x,y,z) \rightarrow (-3,1,2)}\frac{\ln z}{xy-z}$$

Calculus and Analysis

### Find derivatives for the functions. Assume a, b, c, and k are constants. $$\displaystyle{y}'={\left({17}{x}+{24}{x}^{{{\frac{{{1}}}{{{2}}}}}}\right)}'$$

Exponential models

### Sociologists have found that information spreads among a population at an exponential rate. Suppose that the function $$y=525(1−e^{−0.038}t)$$ models the number of people in a town of 525 people who have heard news within t hours of its distribution. How many people will have heard about the opening of a new grocery store within 24 hours of the announcement?

Rational functions

Modeling