Explanation Given information : f ( x ) = x 2 + 3 x 2 − 5 Formula needed : Quotient Rule - d d x ( f g ) = g d f d x − f d g d x g 2 Calculation : Let us take u = x 2 + 3 x 2 − 5 ; f ( x ) = u differentiate function with respect to u , d f d u = d d u ( u ) = 1 2 u differentiate u with respect to x , d u d x = d d x ( x 2 + 3 x 2 − 5 ) Apply quotient rule, d u d x = ( x 2 − 5 ) d d x ( x 2 + 3 ) − ( x 2 + 3 ) d d x (

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Chapter 3.5, Problem 29PS

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Tocalculate : Derivative of f(x)

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Chapter 3.5, Problem 28PS

Chapter 3.5, Problem 30PS

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3.1 Limits 1. If lim f(x)=-6 and lim f(x)=5, then lim f(x). Explain your choice. x+3° x+3* x+3 (a) Is 5 (c) Does not exist (b) is 6 (d) is infinite

1 pts Let F and G be vector fields such that ▼ × F(0, 0, 0) = (0.76, -9.78, 3.29), G(0, 0, 0) = (−3.99, 6.15, 2.94), and G is irrotational. Then sin(5V (F × G)) at (0, 0, 0) is Question 1 -0.246 0.072 -0.934 0.478 -0.914 -0.855 0.710 0.262 .

2. Answer the following questions. (A) [50%] Given the vector field F(x, y, z) = (x²y, e", yz²), verify the differential identity Vx (VF) V(V •F) - V²F (B) [50%] Remark. You are confined to use the differential identities. Let u and v be scalar fields, and F be a vector field given by F = (Vu) x (Vv) (i) Show that F is solenoidal (or incompressible). (ii) Show that G = (uvv – vVu) is a vector potential for F.

Chapter 3 Solutions

Student's Solution and Survival Manual for Calculus

Ch. 3.1 - Prob. 1PS Ch. 3.1 - Prob. 2PS Ch. 3.1 - Prob. 3PS Ch. 3.1 - Prob. 4PS Ch. 3.1 - Prob. 5PS Ch. 3.1 - Prob. 6PS Ch. 3.1 - Prob. 7PS Ch. 3.1 - Prob. 8PS Ch. 3.1 - Prob. 9PS Ch. 3.1 - Prob. 10PS

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Tocalculate : Derivative of f ( x )

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Chapter 3 Solutions