Program Description: Purpose of the problem is to graph the staircase function f ( t ) = n if n − 1 ≤ t < n , n = 1 , 2 , 3 , … .

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Answer 1

Question

Chapter 7.1, Problem 39P

(a)

Program Plan Intro

Program Description: Purpose of the problem is to graph the staircase function f(t)=n if n−1≤t<n, n=1,2,3,… .

(b)

Program Plan Intro

Program Description: Purpose of the problem is to show that staircase function can be described as f(t)=∑n=0∞u(t−n) .

(c)

Program Plan Intro

Program Description: Purpose of the problem is to show that Laplace transform of staircase function is L{f(t)}=1s(1−e −s) .

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Under certain conditions, the number of diseased cells N(t) at time t increases at a rate N'(t) = Aekt, where A is the rate of increase at time 0 (in cells per day) and k is a constant. (a) Suppose A = 60, and at 3 days, the cells are growing at a rate of 180 per day. Find a formula for the number of cells after t days, given that 200 cells are present at t = 0. (b) Use your answer from part (a) to find the number of cells present after 8 days. (a) Find a formula for the number of cells, N(t), after t days. N(t) = (Round any numbers in exponents to five decimal places. Round all other numbers to the nearest tenth.)

The marginal revenue (in thousands of dollars) from the sale of x handheld gaming devices is given by the following function. R'(x) = 4x (x² +26,000) 2 3 (a) Find the total revenue function if the revenue from 125 devices is $17,939. (b) How many devices must be sold for a revenue of at least $50,000? (a) The total revenue function is R(x) = (Round to the nearest integer as needed.) given that the revenue from 125 devices is $17,939.

Use substitution to find the indefinite integral. S 2u √u-4 -du Describe the most appropriate substitution case and the values of u and du. Select the correct choice below and fill in the answer boxes within your choice. A. Substitute u for the quantity in the numerator. Let v = , so that dv = ( ) du. B. Substitute u for the quantity under the root. Let v = u-4, so that dv = (1) du. C. Substitute u for the quantity in the denominator. Let v = Use the substitution to evaluate the integral. so that dv= ' ( du. 2u -du= √√u-4

Answer 2

Question

Chapter 7.1, Problem 39P

(a)

Program Plan Intro

Program Description: Purpose of the problem is to graph the staircase function f(t)=n if n−1≤t<n, n=1,2,3,… .

(b)

Program Plan Intro

Program Description: Purpose of the problem is to show that staircase function can be described as f(t)=∑n=0∞u(t−n) .

(c)

Program Plan Intro

Program Description: Purpose of the problem is to show that Laplace transform of staircase function is L{f(t)}=1s(1−e −s) .

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Answer 3

Question

Chapter 7.1, Problem 39P

(a)

Program Plan Intro

Program Description: Purpose of the problem is to graph the staircase function f(t)=n if n−1≤t<n, n=1,2,3,… .

(b)

Program Plan Intro

Program Description: Purpose of the problem is to show that staircase function can be described as f(t)=∑n=0∞u(t−n) .

(c)

Program Plan Intro

Program Description: Purpose of the problem is to show that Laplace transform of staircase function is L{f(t)}=1s(1−e −s) .

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 4

Question

Chapter 7.1, Problem 39P

(a)

Program Plan Intro

Program Description: Purpose of the problem is to graph the staircase function f(t)=n if n−1≤t<n, n=1,2,3,… .

(b)

Program Plan Intro

Program Description: Purpose of the problem is to show that staircase function can be described as f(t)=∑n=0∞u(t−n) .

(c)

Program Plan Intro

Program Description: Purpose of the problem is to show that Laplace transform of staircase function is L{f(t)}=1s(1−e −s) .

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 5

Chapter 7.1, Problem 39P

(a)

Program Plan Intro

Program Description: Purpose of the problem is to graph the staircase function f(t)=n if n−1≤t<n, n=1,2,3,… .

(b)

Program Plan Intro

Program Description: Purpose of the problem is to show that staircase function can be described as f(t)=∑n=0∞u(t−n) .

(c)

Program Plan Intro

Program Description: Purpose of the problem is to show that Laplace transform of staircase function is L{f(t)}=1s(1−e −s) .

Answer 6

Chapter 7.1, Problem 39P

(a)

Program Plan Intro

Program Description: Purpose of the problem is to graph the staircase function f(t)=n if n−1≤t<n, n=1,2,3,… .

Answer 7

Chapter 7.1, Problem 39P

(a)

Program Plan Intro

Program Description: Purpose of the problem is to graph the staircase function f(t)=n if n−1≤t<n, n=1,2,3,… .

Answer 8

(b)

Program Plan Intro

Program Description: Purpose of the problem is to show that staircase function can be described as f(t)=∑n=0∞u(t−n) .

Answer 9

(b)

Program Plan Intro

Program Description: Purpose of the problem is to show that staircase function can be described as f(t)=∑n=0∞u(t−n) .

Answer 10

(c)

Program Plan Intro

Program Description: Purpose of the problem is to show that Laplace transform of staircase function is L{f(t)}=1s(1−e −s) .

Answer 11

(c)

Program Plan Intro

Program Description: Purpose of the problem is to show that Laplace transform of staircase function is L{f(t)}=1s(1−e −s) .

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 7.1 - Apply the definition in (1) to find directly tile...Ch. 7.1 - Prob. 2P Ch. 7.1 - Prob. 3P Ch. 7.1 - Prob. 4P Ch. 7.1 - Prob. 5P Ch. 7.1 - Prob. 6P Ch. 7.1 - Prob. 7P Ch. 7.1 - Prob. 8P Ch. 7.1 - Prob. 9P Ch. 7.1 - Prob. 10P

Program Description: Purpose of the problem is to graph the staircase function f ( t ) = n if n − 1 ≤ t < n , n = 1 , 2 , 3 , … .

Solution Summary: The author explains how to graph the staircase function f(t) for first four positive integers.

Concept explainers

Program Description: Purpose of the problem is to graph the staircase function f(t)=n if n−1≤t<n, n=1,2,3,… .

Program Description: Purpose of the problem is to show that staircase function can be described as f(t)=∑n=0∞u(t−n) .

Program Description: Purpose of the problem is to show that Laplace transform of staircase function is L{f(t)}=1s(1−e −s) .

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Chapter 7 Solutions

Program Description: Purpose of the problem is to graph the staircase function f ( t ) = n if n − 1 ≤ t &lt; n , n = 1 , 2 , 3 , … .

Solution Summary: The author explains how to graph the staircase function f(t) for first four positive integers.

Concept explainers

Program Description: Purpose of the problem is to graph the staircase function f(t)=n if n−1≤t<n, n=1,2,3,… .

Program Description: Purpose of the problem is to show that staircase function can be described as f(t)=∑n=0∞u(t−n) .

Program Description: Purpose of the problem is to show that Laplace transform of staircase function is L{f(t)}=1s(1−e −s) .

Want to see the full answer?

Chapter 7 Solutions

Program Description: Purpose of the problem is to graph the staircase function f ( t ) = n if n − 1 ≤ t < n , n = 1 , 2 , 3 , … .