A conjecture about the growth rate of y 1 = e x and y = x n , where n is a natural number and x approaches to ∞ .

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Chapter 5, Problem 3PS

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A conjecture about the growth rate of y1=ex and y=xn, where n is a natural number and x approaches to ∞.

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The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after θ seconds can be described by the function f(θ) = 2sinθ + √2.Part A: Determine all values where the pogo stick's spring will be equal to its non-compressed length. Part B: If the angle was doubled, that is θ became 2θ, what are the solutions in the interval [0, 2π)? How do these compare to the original function?Part C: A toddler is jumping on another pogo stick whose length of its spring can be represented by the function g(θ) = 1 cos^2θ + √2. At what times are the springs from the original pogo stick and the toddler's pogo stick lengths equal?

Students were asked to prove the identity (sec x)(csc x) = cot x + tan x. Two students' work is given.Student AStep 1:1/Cos x * 1/sin x = cot x + tan xStep 2: 1/cos x sin x = cot x + tan xStep 3: (cos^2 x + sin^2 x)/cos x sin x = cot x + tan xStep 4: cos^2 x/cos x sin x + sin^2x/cos x sin x= cot x + tan xStep 5: cos x/sin x + sin x/cos x = cot x + tan xStep 6: cot x + tan x = cot x + tan xStudent BStep 1: sec x csc x = cos x/ sin xStep 2: sec x csc x = cos^2x/cos x sin x + sin^2x/cos x sin xStep 3: sec x csc x = cos^2x + sin^2x/cos x sin xStep 4: sec x csc x = 1/cos x sin xStep 5: sec x csc x = (1/cos x), (1/sin x)Step 6: sec x csc x = sec x csc xPart A: Did either student verify the identity properly? Explain why or why not. Part B: Name two identities that were used in Student A's verification and the steps they appear in.

Let sinθ = 2√2/5 and π/2 < θ < πPart A: Determine the exact value of cos 2θ.Part B: Determine the exact value of sin(θ/2)

Answer 2

Question

Chapter 5, Problem 3PS

To determine

A conjecture about the growth rate of y1=ex and y=xn, where n is a natural number and x approaches to ∞.

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Answer 3

Question

Chapter 5, Problem 3PS

To determine

A conjecture about the growth rate of y1=ex and y=xn, where n is a natural number and x approaches to ∞.

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Answer 4

Question

Chapter 5, Problem 3PS

To determine

A conjecture about the growth rate of y1=ex and y=xn, where n is a natural number and x approaches to ∞.

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Answer 5

Chapter 5, Problem 3PS

To determine

A conjecture about the growth rate of y1=ex and y=xn, where n is a natural number and x approaches to ∞.

Answer 6

Chapter 5, Problem 3PS

To determine

A conjecture about the growth rate of y1=ex and y=xn, where n is a natural number and x approaches to ∞.

Answer 7

Chapter 5, Problem 3PS

To determine

A conjecture about the growth rate of y1=ex and y=xn, where n is a natural number and x approaches to ∞.

Answer 8

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Answer 9

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A conjecture about the growth rate of y 1 = e x and y = x n , where n is a natural number and x approaches to ∞ .

Solution Summary: The author explains that the growth rate of exponential function, y_1=ex, is greater than that of the polynomial function.

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A conjecture about the growth rate of y1=ex and y=xn, where n is a natural number and x approaches to ∞.

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