
Calculus Combo
14th Edition
ISBN: 9781464151088
Author: Associate Professor Laura Taalman, Peter Kohn
Publisher: W.H. Freeman & Company
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Chapter 5.4, Problem 11C
To determine
Decribe the strategy to solve the integral.
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18. Using the method of variation of parameter, a particular solution to y′′ + 16y = 4 sec(4t) isyp(t) = u1(t) cos(4t) + u2(t) sin(4t). Then u2(t) is equal toA. 1 B. t C. ln | sin 4t| D. ln | cos 4t| E. sec(4t)
Question 4. Suppose you need to know an equation of the tangent plane to a
surface S at the point P(2, 1, 3). You don't have an equation for S but you know
that the curves
r1(t) = (2 + 3t, 1 — t², 3 − 4t + t²)
r2(u) = (1 + u², 2u³ − 1, 2u + 1)
both lie on S.
(a) Check that both r₁ and r2 pass through the point P.
1
(b) Give the expression of the 074 in two ways
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⚫ in terms of 32 and 33 using the chain rule
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⚫ in terms of t using the expression of z(t) in the curve r1
(c) Similarly, give the expression of the 22 in two ways
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⚫ in terms of oz and oz using the chain rule
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in terms of u using the expression of z(u) in the curve r2
(d) Deduce the partial derivative 32 and 33 at the point P and the equation of
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the tangent plane
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