Explanation Given information: Fundamental theorem of Calculus: If f is ………….on [ a , b ] ,and if ‘F’ is any …………………….of f ,then ∫ a b f ( x ) d x = .................. Concept and Formula Used: Fundamental theorem of calculus. Calculation: The given statement is Fundamental theorem of Calculus: If f is ………….on [ a , b ] ,and if ‘F’ is any …………………….of f ,then ∫ a b f ( x ) d x = .................. According to fundamental theorem of Calculus “If g is continuous on [ c , d ] and if ‘G’ is any antiderivative of g ,then

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 4, Problem 2T

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To Fill: In the blanks Fundamental theorem of Calculus: If f is ………….on [a,b] and if ‘F’ is any …………………….of f ,then ∫abf(x)dx=..................

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Chapter 4, Problem 1T

Chapter 4, Problem 3T

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6. The largest interval in which the solution of (cos t)y′′ +t^2y′ − (5/t)y = e^t/(t−3) , y(1) = 2, y′(1) = 0is guaranteed to exist by the Existence and Uniqueness Theorem is:A. (0, ∞) B. (π/2, 3) C. (0,π/2) D. (0, π) E. (0, 3)

12. For the differential equation in the previous question, what is the correct form for a particularsolution?A. yp = Ae^t + Bt^2 B. yp = Ae^t + Bt^2 + Ct + DC. yp = Ate^t + Bt^2 D. yp = Ate^t + Bt^2 + Ct + D Previous differential equation y′′ − 4y′ + 3y = e^t + t^2

16. The appropriate form for the particular solution yp(x) of y^(3) − y′′ − 2y′ = x^2 + e^2x isA. yp(x) = Ax^2 + Bx + C + De^2x B. yp(x) = Ax^3 + Bx^2 + Cx + Dxe^2xC. yp(x) = Ax^2 +Be^2x D. yp(x) = A+Be^2x +Ce^−x E. yp(x) = Ax^2 +Bx+C +(Dx+E)e^2x

Chapter 4 Solutions

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In the blanks Fundamental theorem of Calculus: If f is ………….on [ a , b ] and if ‘F’ is any …………………….of f ,then ∫ a b f ( x ) d x = ..................

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To Fill: In the blanks Fundamental theorem of Calculus: If f is ………….on [a,b] and if ‘F’ is any …………………….of f ,then ∫abf(x)dx=..................

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Chapter 4 Solutions