###### Precalculus

582 SOLVED PROBLEMS

Question: P.6.2

## Simplifying Rational Expressions Simplify: a. x³ + x²/x + 1 b. x² + 6x + 5/x² – 25. ...

a. \frac{x^3+x^2}{x+1}=\frac{x^2(x+1)}{x+1}...
Question: 4.2.8

## Evaluating Trigonometric Functions with a Calculator Use a calculator to find the value to four decimal places: a. cos π/4 b. cot 1.2. ...

Scientific Calculator Solution \begin{matri...
Question: 1.3.8

## Evaluating and Simplifying a Difference Quotient If f(x) = 2x² – x + 3, find and simplify each expression: a. f(x + h) b. f(x + h) – f(x)/h, h ≠ 0. ...

a. We find f(x + h) by replacing x with x + h each...
Question: 8.4.5

## Using the Inverse of a Matrix to Solve a System Solve the system by using A^-1, the inverse of the coefficient matrix: {x – y + z = 2 -2y + z = 2 -2x -3y = 1/2. ...

The linear system can be written as The solution ...
Question: 8.4.4

## Finding the Multiplicative Inverse of a 3 × 3 Matrix Find the multiplicative inverse of A = [1 -1 1 0 -2 1 -2 -3 0]. ...

Step 1 Form the augmented matrix \left[A \m...
Question: 11.3.2

## Determining Where a Piecewise Function Is Discontinuous Determine for what numbers x, if any, the following function is discontinuous: f(x) = {x + 2 if x ≤ 0 2 if 0 1 ...

First, let’s determine whether each of the three p...
Question: 8.1.4

## Gaussian Elimination with Back-Substitution Use matrices to solve the system: {2w + x + 3y – z = 6 w – x + 2y – 2z = -1 w – x – y + z = -4 -w + 2x – 2y – z = -7. ...

Step 1 Write the augmented matrix for the system. ...
Question: 6.3.7

## Converting Equations from Polar to Rectangular Form Convert each polar equation to a rectangular equation in x and y: a. r = 5 b. θ = π/4 c. r = 3 csc θ d. r = -6 cos θ. ...

In each case, let’s express the rectangular equati...
Question: 4.1.4

## Drawing Angles in Standard Position Draw and label each angle in standard position: a. θ = π/4 b. α = 5π/4 c. β = -3π/4 d. γ = 9π/4. ...

Because we are drawing angles in standard position...
Question: 2.4.1