Explanation Given: The function f ( x ) is as follows: f ( x ) = { e − 1 x 2 for x ≠ 0 0 for x = 0 The limit lim t → ∞ t k e − t 2 = 0 for all k . Proof: Simplify the expression lim x → 0 f ( x ) x k as shown below: lim x → 0 f ( x ) x k = lim x → 0 e − 1 x 2 x k = lim x → 0 1 x k e 1 x

ACHIEVE FOR CALCULUS 1 TERM >CSI CUSTOM<

4th Edition

ISBN: 9781319411657

Author: Rogawski

Publisher: MAC HIGHER

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Question

Chapter 4.5, Problem 75E

To determine

To show:

That limx→0f(x)xk=0 for all k.

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Chapter 4.5, Problem 74E

Chapter 4.5, Problem 76E

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4 In the integral dxf1dy (7)², make the change of variables x = ½(r− s), y = ½(r + s), and evaluate the integral. Hint: Find the limits on r and s by sketching the area of integration in the (x, y) plane along with the r and s axes, and then show that the same area can be covered by s from 0 to r and r from 0 to 1.

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can you solve this question using the right triangle method and explain the steps used along the way

Chapter 4 Solutions

ACHIEVE FOR CALCULUS 1 TERM >CSI CUSTOM<

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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