Explanation Given : The inequality 0 ≤ sin x ≤ x for x ≥ 0 Calculation : Step 1: Since, sin ( x y ) ≤ x y , we get ∫ 0 1 ∫ 0 1 sin ( x y ) d x d y ≤ ∫ 0 1 ∫ 0 1 x y d x d y To determine (b) The value of the double integral ∫ 0 1 ∫ 0 1 sin ( x y ) d x d y to three decimal places using a computer algebra system.

4th Edition

ISBN: 9781319279813

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 15.2, Problem 60E

To determine

(a)

The mathematical proof the relation $\int_{0}^{1} \int_{0}^{1} \sin (x y) d x d y \leq \frac{1}{4}$ using the inequality $0 \leq \sin x \leq x$ for $x \geq 0$

To determine

(b)

The value of the double integral $\int_{0}^{1} \int_{0}^{1} \sin (x y) d x d y$ to three decimal places using a computer algebra system.

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Chapter 15.2, Problem 59E

Chapter 15.2, Problem 61E

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For the following function f and real number a, a. find the slope of the tangent line mtan = f' (a), and b. find the equation of the tangent line to f at x = a. f(x)= 2 = a = 2 x2 a. Slope: b. Equation of tangent line: y

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Chapter 15 Solutions

CALCULUS:EARLY TRANS.-SAPLINGPLUS

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Knowledge Booster

(a) The mathematical proof the relation ∫ 0 1 ∫ 0 1 sin ( x y ) d x d y ≤ 1 4 using the inequality 0 ≤ sin x ≤ x for x ≥ 0

(a) The mathematical proof the relation ∫01∫01sin(xy)dxdy≤14 using the inequality 0≤sinx≤x for x≥0

(b) The value of the double integral ∫01∫01sin(xy)dxdy to three decimal places using a computer algebra system.

Want to see the full answer?

Chapter 15 Solutions

(a)

The mathematical proof the relation $\int_{0}^{1} \int_{0}^{1} \sin (x y) d x d y \leq \frac{1}{4}$ using the inequality $0 \leq \sin x \leq x$ for $x \geq 0$

(b)

The value of the double integral $\int_{0}^{1} \int_{0}^{1} \sin (x y) d x d y$ to three decimal places using a computer algebra system.