Explanation Given: The given functions are f ( x ) = e x and g ( x ) = x 2 Concept used: The value of g ( x ) at x = a will be obtained by substituting a for x in g ( x ) . Substitute g ( a ) for x in f ( x ) to get the value of f ( g ( a ) ) . Calculation: Consider the function g ( x ) = x 2 . Substitute 1 for x in g ( x ) = x 2 To determine (b) To find the function g ( f ( 1 ) ) . To determine (c) To find the function f ( g ( x ) ) . To determine (d) To find the function: g ( f ( x ) ) To determine (e) To find the function: f ( t ) g ( t )

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Differential Equations

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Chapter 1.8, Problem 9P

To determine

(a)

To find the function f(g(1)).

To determine

(b)

To find the function g(f(1)).

To determine

(c)

To find the function f(g(x)).

To determine

(d)

To find the function:

g(f(x))

To determine

(e)

To find the function:

f(t)g(t)

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Chapter 1.8, Problem 8P

Chapter 1.8, Problem 10P

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2. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.4.006.MI. Use the Table of Integrals to evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) 7y2 y² 11 dy Need Help? Read It Master It SUBMIT ANSWER 3. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.4.009. Use the Table of Integrals to evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) tan³(12/z) dz Need Help? Read It Watch It SUBMIT ANSWER 4. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.4.014. Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) 5 sinб12x dx Need Help? Read It

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y"-9y+20y= 80t-156 y(0) = −6, y'(0) = 5 y(t) =

Chapter 1 Solutions

APPLIED CALCULUS (WILEY PLUS)

Ch. 1.1 - Prob. 1P Ch. 1.1 - Prob. 2P Ch. 1.1 - Prob. 3P Ch. 1.1 - Prob. 4P Ch. 1.1 - Prob. 5P Ch. 1.1 - Prob. 6P Ch. 1.1 - Prob. 7P Ch. 1.1 - Prob. 8P Ch. 1.1 - Prob. 9P Ch. 1.1 - Prob. 10P

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(a) To find the function f ( g ( 1 ) ) .

Solution Summary: The author calculates the value of g(x) at x=a by substituting 1 for 2.

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(a)

To find the function f(g(1)).

(b)

To find the function g(f(1)).

(c)

To find the function f(g(x)).

(d)

To find the function:

g(f(x))

(e)

To find the function:

f(t)g(t)

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Chapter 1 Solutions

(a) To find the function f ( g ( 1 ) ) .

Solution Summary: The author calculates the value of g(x) at x=a by substituting 1 for 2.

Concept explainers

Videos

(a) To find the function f(g(1)).

(b) To find the function g(f(1)).

(c) To find the function f(g(x)).

(d) To find the function: g(f(x))

(e) To find the function: f(t)g(t)

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Chapter 1 Solutions

(a)

To find the function f(g(1)).

(b)

To find the function g(f(1)).

(c)

To find the function f(g(x)).

(d)

To find the function:

g(f(x))

(e)

To find the function:

f(t)g(t)