BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 1, Problem 8RCC

(a)

To determine

To sketch: The rough graph of the function y=sinx.

Expert Solution

Explanation of Solution

The rough graph of y=sinx is roughly drawn and shown below in Figure 1.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1, Problem 8RCC , additional homework tip  1

From Figure 1, it is observed that the sine function is defined on 1sinx1 and is a periodic function with period 2π,sin(x+2π)=sin(x).

(b)

To determine

To sketch: The rough graph of the function y=tanx.

Expert Solution

Explanation of Solution

The rough graph of y=tanx is roughly drawn and shown below in Figure 2.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1, Problem 8RCC , additional homework tip  2

From Figure 2, it is observed that the tan function is undefined when cos x = 0 and is a periodic with period π,tan(x+π)=tan(x).

(c)

To determine

To sketch: The rough graph of the function y=ex.

Expert Solution

Explanation of Solution

The rough graph of y=ex is roughly drawn and shown below in Figure 3.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1, Problem 8RCC , additional homework tip  3

From Figure 3, it is observed that the exponential function is an increasing function with the domain (,) and the range (0,).

(d)

To determine

To sketch: The rough graph of the function y=lnx.

Expert Solution

Explanation of Solution

The rough graph of y=lnx is roughly drawn and shown below in Figure 4.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1, Problem 8RCC , additional homework tip  4

From Figure 4, it is observed that the logarithmic function is an increasing function with the domain (0,) and the range (,). Also, notice that the logarithmic function is a reciprocal of an exponential function.

(e)

To determine

To sketch: The rough graph of the function y=1x.

Expert Solution

Explanation of Solution

The rough graph of y=1x is roughly drawn and shown below in Figure 5.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1, Problem 8RCC , additional homework tip  5

From Figure 5, it is observed that the reciprocal function is an hyperbola with x and y axes as its asymptotes.

(f)

To determine

To sketch: The rough graph of the function y=|x|.

Expert Solution

Explanation of Solution

The rough graph of y=|x| is roughly drawn and shown below in Figure 6.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1, Problem 8RCC , additional homework tip  6

From Figure 6, it is observed that the range of an absolute function is positive y-axis.

(g)

To determine

To sketch: The rough graph of the function y=x.

Expert Solution

Explanation of Solution

The rough graph of y=x is roughly drawn and shown below in Figure 7.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1, Problem 8RCC , additional homework tip  7

From Figure 7, it is observed that the range of the power function with the power 12.

(h)

To determine

To sketch: The rough graph of the function y=tan1x.

Expert Solution

Explanation of Solution

The rough graph of y=tan1x is roughly drawn and shown below in Figure 8.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1, Problem 8RCC , additional homework tip  8

From Figure 8, it is observed that the domain of an inverse tan function is (,) and the range is (π2,π2). Also, notice that the tan function and the inverse of trigonometric function are inverse function of each other. So, they reflect about the y = x.

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