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Chapter 14 Solutions
Calculus: Early Transcendentals, 2nd Edition
- 5. Prove that the equation has no solution in an ordered integral domain.arrow_forwardFind the area between the curves in Exercises 1-28. x=0, x=/4, y=sec2x, y=sin2xarrow_forwardWHite the veD secsand orde equation as is equivalent svstem of hirst order equations. u" +7.5z - 3.5u = -4 sin(3t), u(1) = -8, u'(1) -6.5 Use v to represent the "velocity fumerion", ie.v =(). Use o and u for the rwo functions, rather than u(t) and v(t). (The latter confuses webwork. Functions like sin(t) are ok.) +7.5v+3.5u-4 sin 3t Now write the system using matrices: dt 3.5 7.5 4 sin(3t) and the initial value for the vector valued function is: u(1) v(1) 3.5arrow_forward
- Verify that the Fundamental Theorem for line integrals can be used to evaluate the following line integral, and then evaluate the line integral using this theorem. v(e -* sin y) • dr, where C is the line from (0,0) to (In 3,1t) Select the correct choice below and fill in the answer box to complete your choice as needed. A. The Fundamental Theorem for line integrals can be used to evaluate the line integral because the function is conservative on its domain and has a potential function p(x,y) = (Type an exact answer.) O B. The function is not conservative on its domain, and therefore, the Fundamental Theorem for line integrals cannot be used to evaluate the line integral.arrow_forwardFind div F and curl F if F(x, y, z) = 10e i − 4 cos y j + sin² z k. div F= curl F=arrow_forwarda) Evaluate y? dydx. b) Evaluate the line integral Cos x cos y dx + (1 – sin x sin y) dy - where C is the part of the curve y = sin x from x = 0 to x = T/2.arrow_forward
- a) Evaluate the integrals using appropriate substitutions. dx Sino i) S de u) I Cos?8+ 1 ü) j 1+16x2 b) Evaluate the integrals using Part 1 of the Fundamental Theorem of Calculus. /2(x+ 2 L 4x(1 – x?)dx ii) (x + -) dx Sin2x i) c) Use Part 2 of the Fundamental Theorem of Calculus to find the derivatives. evE dt d d i) ii) Intdt dx dxarrow_forwardSet up, but do not evaluate, an integral that represents the length of the parametric curve Select the correct answer. 10 2x O√₁ +3² (In 3)² dx 5 10 O√T 1 + 3* In 3 dx 5 5 O √1 +3² (In 3)² dx J 10 10 Of 3²* (In 3)² dx 5 √1 + 10² (In 10)² dx y=3*, 5 ≤ x ≤ 10.arrow_forwardEvaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 4 ydx + 3 x²dy, where Cis the square with vertices (0,0), (1, 0), (1, 1), and (0, 1) oriented counterclockwise. 643° dx + 3 x°dy = iarrow_forward
- Use Green's Theorem to evaluate the line integral. Lex cos(2y) dx – 2ex sin(2y) dy C: x2 + y2 = a²arrow_forwardShow that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals to find its value. NOTE: Enter the exact answer. r(5,7) 2xe dx + x*edy (0,0)arrow_forwardEvaluate F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. (3yi + 3xj) · dr C: smooth curve from (0, 0) to (3, 2)arrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
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