CALCULUS: EARLY TRANS. (LL)W/WEBASSIGN
8th Edition
ISBN: 9780357019788
Author: Stewart
Publisher: CENGAGE L
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Chapter H, Problem 30E
To determine
To find: The polar form of
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Evaluate the definite integral using the given integration limits and the limits obtained by trigonometric substitution.
14
x²
dx
249
(a) the given integration limits
(b) the limits obtained by trigonometric substitution
Assignment #1
Q1: Test the following series for convergence. Specify the test you use:
1
n+5
(-1)n
a) Σn=o
√n²+1
b) Σn=1 n√n+3
c) Σn=1 (2n+1)3
3n
1
d) Σn=1 3n-1
e) Σn=1
4+4n
Chapter H Solutions
CALCULUS: EARLY TRANS. (LL)W/WEBASSIGN
Ch. H - Prob. 1ECh. H - Prob. 2ECh. H - Prob. 3ECh. H - Prob. 4ECh. H - Prob. 5ECh. H - Prob. 6ECh. H - Prob. 7ECh. H - Evaluate the expression and write your answer in...Ch. H - Prob. 9ECh. H - Prob. 10E
Ch. H - Prob. 11ECh. H - Prob. 12ECh. H - Prob. 13ECh. H - Evaluate the expression and write your answer in...Ch. H - Prob. 15ECh. H - Prob. 16ECh. H - Prob. 17ECh. H - Prove the following properties of complex numbers....Ch. H - Prob. 19ECh. H - Prob. 20ECh. H - Prob. 21ECh. H - Find all solutions of the equation. 22. 2x2 2x +...Ch. H - Prob. 23ECh. H - Find all solutions of the equation. 24....Ch. H - Write the number in polar form with argument...Ch. H - Prob. 26ECh. H - Prob. 27ECh. H - Prob. 28ECh. H - Write the number in polar form with argument...Ch. H - Prob. 30ECh. H - Prob. 31ECh. H - Prob. 32ECh. H - Find the indicated power using De Moivres Theorem....Ch. H - Prob. 34ECh. H - Prob. 35ECh. H - Prob. 36ECh. H - Prob. 37ECh. H - Prob. 38ECh. H - Prob. 39ECh. H - Prob. 40ECh. H - Prob. 41ECh. H - Prob. 42ECh. H - Prob. 43ECh. H - Prob. 44ECh. H - Prob. 45ECh. H - Prob. 46ECh. H - Prob. 47ECh. H - Use Eulers formula to prove the following formulas...Ch. H - If u(x) = f(x) + ig(x) is a complex-valued...Ch. H - (a) If u is a complex-valued function of a real...
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Evaluate ſ √9-x2 -dx. x2 a) C 9-x2 √9-x2 - x2 b) C - x x arcsin ½-½ c) C + √9 - x² + arcsin x d) C + √9-x2 x2 13. Find the indefinite integral S cos³30 √sin 30 dᎾ . 2√√sin 30 (5+sin²30) √sin 30 (3+sin²30) a) C+ √sin 30(5-sin²30) b) C + c) C + 5 5 5 10 d) C + 2√√sin 30 (3-sin²30) 2√√sin 30 (5-sin²30) e) C + 5 15 14. Find the indefinite integral ( sin³ 4xcos 44xdx. a) C+ (7-5cos24x)cos54x b) C (7-5cos24x)cos54x (7-5cos24x)cos54x - 140 c) C - 120 140 d) C+ (7-5cos24x)cos54x e) C (7-5cos24x)cos54x 4 4 15. Find the indefinite integral S 2x2 dx. ex - a) C+ (x²+2x+2)ex b) C (x² + 2x + 2)e-* d) C2(x²+2x+2)e¯* e) C + 2(x² + 2x + 2)e¯* - c) C2x(x²+2x+2)e¯*arrow_forward4. Which substitution would you use to simplify the following integrand? S a) x = sin b) x = 2 tan 0 c) x = 2 sec 3√√3 3 x3 5. After making the substitution x = = tan 0, the definite integral 2 2 3 a) ៖ ស្លឺ sin s π - dᎾ 16 0 cos20 b) 2/4 10 cos 20 π sin30 6 - dᎾ c) Π 1 cos³0 3 · de 16 0 sin20 1 x²√x²+4 3 (4x²+9)2 π d) cos²8 16 0 sin³0 dx d) x = tan 0 dx simplifies to: de 6. In order to evaluate (tan 5xsec7xdx, which would be the most appropriate strategy? a) Separate a sec²x factor b) Separate a tan²x factor c) Separate a tan xsecx factor 7. Evaluate 3x x+4 - dx 1 a) 3x+41nx + 4 + C b) 31n|x + 4 + C c) 3 ln x + 4+ C d) 3x - 12 In|x + 4| + C x+4arrow_forward1. Abel's Theorem. The goal in this problem is to prove Abel's theorem by following a series of steps (each step must be justified). Theorem 0.1 (Abel's Theorem). If y1 and y2 are solutions of the differential equation y" + p(t) y′ + q(t) y = 0, where p and q are continuous on an open interval, then the Wronskian is given by W (¥1, v2)(t) = c exp(− [p(t) dt), where C is a constant that does not depend on t. Moreover, either W (y1, y2)(t) = 0 for every t in I or W (y1, y2)(t) = 0 for every t in I. 1. (a) From the two equations (which follow from the hypotheses), show that y" + p(t) y₁ + q(t) y₁ = 0 and y½ + p(t) y2 + q(t) y2 = 0, 2. (b) Observe that Hence, conclude that (YY2 - Y1 y2) + P(t) (y₁ Y2 - Y1 Y2) = 0. W'(y1, y2)(t) = yY2 - Y1 y2- W' + p(t) W = 0. 3. (c) Use the result from the previous step to complete the proof of the theorem.arrow_forward2. Observations on the Wronskian. Suppose the functions y₁ and y2 are solutions to the differential equation p(x)y" + q(x)y' + r(x) y = 0 on an open interval I. 1. (a) Prove that if y₁ and y2 both vanish at the same point in I, then y₁ and y2 cannot form a fundamental set of solutions. 2. (b) Prove that if y₁ and y2 both attain a maximum or minimum at the same point in I, then y₁ and Y2 cannot form a fundamental set of solutions. 3. (c) show that the functions & and t² are linearly independent on the interval (−1, 1). 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