Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 13.3, Problem 47PS
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6. Let f(x) be the function given to the right. Calculate each of
the following integrals.
(a) √² ƒ(
1².
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(c) [f(x) dx = 3₁
-3.5
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(e) [² f(x) dx = 5.2
3
(b) f(x) dx = 1,5
6
(d) f(x) dx =
So
10
(f) f f(x) dx =
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1 2 3 4 5 6
420
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8 f
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for the function f (x, y) = ea sin (ay).
7. Let f(x + iy) = (3x?y – y³) + i(3xy² – x³). Decide if f (x + iy) is
differentiable and if it is, then find its derivative f'(x + iy).
Chapter 13 Solutions
Calculus
Ch. 13.1 - Prob. 1PSCh. 13.1 - Prob. 2PSCh. 13.1 - Prob. 3PSCh. 13.1 - Prob. 4PSCh. 13.1 - Prob. 5PSCh. 13.1 - Prob. 6PSCh. 13.1 - Prob. 7PSCh. 13.1 - Prob. 8PSCh. 13.1 - Prob. 9PSCh. 13.1 - Prob. 10PS
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- 5. Use Part one of the fundamental theorem of calculus to find the derivative of the following functions. a. b. C. d. g(x) = 9 (1) = [² | 9'(s) = h'(x)= g(y) = -fe 1 ³+3 h (r) = Sove dt sin 3t dt arctan Ốt dt y = frtan √5t+ √t dtarrow_forward3. Show that the complex function f(z)= cscz =1/ sinz satisfies the Cauchy-Riemann condition. Find the derivative df(2) dzarrow_forward1. Find the gradicnt of the following functions (here, i = v-1, and A is a constant) (a) f (x) = 3x. (b) ƒ (x, t) = 4c*² + 7t². (c) ƒ (z) = 623 (d) ƒ (2) = Acikz (e) f (x, y) = Ac k(x²+y²). + 7.arrow_forward
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