To determine To graph: The function, which is continuous and differentiable everywhere except at x = − 1 , where it has a vertical asymptote, decreasing everywhere, concave downward on ( − ∞ , − 1 ) and ( 1 , 2 ) , concave upward on ( − 1 , 1 ) and ( 2 , ∞ ) . Explanation Given: The given properties are: (a) Continuous and differentiable everywhere except at x = − 1 , where it has a vertical asymptote (b) Decreasing everywhere it is defined (c) Concave downward on ( − ∞ , − 1 ) and ( 1 , 2 ) . (d) Concave upward on ( − 1 , 1 ) and ( 2 , ∞ ) . Calculation: Here given that the graph is continuous and differentiable everywhere except at x = − 1 , where it has a vertical asymptote, means the graph will break at x = − 1 . Also given that the graph is decreasing everywhere, means that the graph has negative slope everywhere in the domain of the function

MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

11th Edition

ISBN: 9781323751671

Author: Lial

Publisher: PEARSON C

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Chapter 12.6, Problem 28E

To determine

To graph: The function, which is continuous and differentiable everywhere except at x=−1, where it has a vertical asymptote, decreasing everywhere, concave downward on (−∞,−1) and (1,2), concave upward on (−1,1) and (2,∞).

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Chapter 12.6, Problem 27E

Chapter 12.6, Problem 29E

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Solve the following inhomogeneous wave equation with initial data. Utt-Uxx = 2, x = R U(x, 0) = 0 Ut(x, 0): = COS X

Could you please solve this question on a note book. please dont use AI because this is the third time i upload it and they send an AI answer. If you cant solve handwritten dont use the question send it back. Thank you.

(a) Write down the general solutions for the wave equation Utt - Uxx = 0. (b) Solve the following Goursat problem Utt-Uxx = 0, x = R Ux-t=0 = 4x2 Ux+t=0 = 0 (c) Describe the domain of influence and domain of dependence for wave equations. (d) Solve the following inhomogeneous wave equation with initial data. Utt - Uxx = 2, x ЄR U(x, 0) = 0 Ut(x, 0) = COS X

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MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

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