What change of variables is suggested by an integral containing * Vx² – 4? O a cosø O none of the choices O a tanø O a secø

Q: 1. Evaluate the following limits. 2 - V2x + 10 a. lim 1-3 x2 + x – 6 4x – 7 1 lim с. -1- (3r2 – 2r…

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Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

A: We need to find surface integral.

Q: x² + 4x – 5 dx = Using Trigonometric Substitution :| f(e)de find the new limits of integration. x+2…

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Q: Find the area of the part of the sphere x2 + y2 + z2 = 100z that lies inside the paraboloid z = x2 +…

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Q: /9- x² Consider dy using Trigonometric Substitution what is dx ? 3 sec e de 3 sec? e de 3 cos e de 3…

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Q: find the inverse laplace transform

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Q: 4. x2(y + 1)dx + y² (x – 1)dy = 0

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Q: Evaluate the itegral by interpreting it in terms of areas. 0. 3 + 100 - x2 ) dx -10

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Q: Find an antiderivative of the function. (a) h(q) = sin(q) H(g) = (b) f(x) = 3eX F(x) =

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Q: Using Integration By Parts, x Arcsec 3x dx = u v- |v du

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Q: Compute the given integral. dr 16x2 + 1 +C

A: Here is the solution:

Q: 1/2 x2 The result of dx is F(b) – F(a); where F(a) and F(b) are real numbers. What is the value of F…

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Q: 4. y²tan y

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Q: Evaluate S. F dr where F(x, y, z) = e'i+ (xe + e²) j+ye²k and C is the line segment from (0, 2, 0)…

A: answer is in next step

Q: (V9- x2 dx using Trigonometric Substitution what is dx ? x2 Consider 3 cos e de 3 sec e tan 0 de 3…

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Q: 5x |(x²+ a) The resulting integral of dx is In +eTan-1X + C, where a, b, d, and e are integers. What…

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Q: Compute f'(a) using f' (a) f(а + h) — f(a) = lim f(x) or f'(a) = lim f(a) for f(x) = 10x³, a = 2.…

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Q: sin- dx 32 cos:주-Scos)+기+ c 35 32 + C COS 7 4 32 32 .coss(수)+C 32 cosS 4 35 Ssin +2 +c

A: The correct option is (3).

Q: (1 + Зx) dx

A: We have to evaluate the integral

Q: 9. Evaluate limf(x) = {"_ (x – 2; x 3 %3D x-3 а. 1 b. -4 с. 3 d. Does not exist 10. Evaluate limf…

A: Our Aim is to evaluate the limit of the expression given below:-limx→3 f(x)=x-2 ; x≤3-4;…

Q: Evaluate the integral Scot? x dx -cot x - x + C cot x + x + C cot x - x + C 1 cot x + C .3 X + O O

A: Topic = Integration

Q: Evaluate the definite integral. sin(4t)dt

A: Here is the solution:

Q: Find f. f"(x) = 6 + 6x + 24x2, f(0) = 2, f(1) = 12 f(x) =

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Q: x² –9 2. dx. Use trigonometric Substitution. .3

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Q: 9- x2 Consider using Trigonometric Substitution what is dx ? x2 3 sec e tan e de 3 sec e de 3 sec2 e…

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Q: Using Integration By Parts, x² Vx? +4 dx =uv- [v du Find Uv- du 3 3 2 -4)2 dx || 4 3 3 2 +4) 2 dx 3…

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Q: Difference of quotient for 1/(x+4)^2

A: The given function,       1x+42

Q: 2x+11 3 1 dx evaluate Consider x² + x-6 dx- x+3 x-2 x+3 X-2 x-2 In +C |x+3 |(x-2)³| In x+3 |x+3 +C…

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Q: Vx2 + 4x - 5 dx = Using Trigonometric Substitution f(e)dA find the new limits of integration. 1. x+2…

A: Let's find.

Q: Evaluate the indefinite integral sin v cOs vdv

A: Given:       ∫3sin4v cosv dv Taking constant out.         =3∫sin4v cosv dv substitute u=sin…

Q: 1. 4x dy – y dx = x²dy %3D

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Q: What are the polar coordinates of the point P shown below? 2 3 4

A: This question is related to coordinate systems, we will solve it using given information.

Q: f2x² Find uv- v du Using Integration By Parts, dx =uv- du UV- | S12 xe 6 x2 dx 3 x2 6x e dx 02

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Q: Evaluate the iterated integral. 6xy2 dx dy

A: We have to evaluate the iterated integral

Q: The loop of the following limacon is produced for which interval of the angle theta?

A: Given:       r=2+4sinθ The first step is to find the angular displacement of the inner loop. To do…

Q: Evaluate the following indefinite integral. da I In(x) Note: Don't forget your C! And be sure to use…

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Q: tan (x) cos (x) 1 tan (x) +tan°(x) + C tan'(x)7tan?(x) +9]+ C 36 O 1 1 tan (x)-tan'(x) + C O…

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Q: Using Integration By Parts, Vx In 2x dx =uv- -Svdu Jv du Find UV- du O 2 늘 xVX In 2x-| Vx dx Xx In…

A: A detailed solution is given below

Q: Using the rule of 72, how long does it take for country X's production to double? 19 years Using the…

A: answer is in next step

Q: /x²+4x – 5 dx Using trigonometric substitution, ƒ (8) dô. x+2 Find the new limits of integration.…

A: Given:        ∫14x2+4x-5x+2dx=∫abfθ dθ         =∫14x+22-9x+2 dx      Apply u-substitution.…

Q: Using Integration By Parts, x Arcsec 3x dx = u v- Jv du - Find u v- Jv du- ㅇ x2 Arcsec 3x-J등 dx x² –…

A: The given integration,        ∫x arcsec(3x)dx

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: Let θ denote the angle between thw ladder and the ground

Q: dx , find f(0) · Using Trigonometric Substitution 3 (x²+ x + 1) 2

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Q: Find the length of the following curve. If you have a grapher, you may want to graph the curve to…

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Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an…

A: We find the local extrma using first derivative test by checking the nature of f'(x) at different…

Q: 2 - V2r + 10 a. lim 1-3 r2 + x – 6

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Solve the following problems. 1. Name and sketch the graph of y² = z in R³. II.

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Q: + y + z = 1 in the first octant.

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Q: Find the point(s) on the graph of f where the tangent line is horizontal. f(«) =x°c* (0, 0), 9, 99…

A: We need to find points where tangent is horizontal.

Q: A stone is dropped from the upper observation deck of a tower, 800 m above the ground. (Assume g =…

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