Evaluate each of the following indefinite integrals: Show complete and detailed solutions. Express your answers in simplest form. ² -4 dt 1.

Q: Determine if the following series is convergent or divergent: 8 n=1 3n2 + 4n + 5 O Convergent O…

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Q: Evaluate:- 4 dx ④ -VR-4-2sec-1(즉)+c A =/x2 – 4 + sec + C (c) =2/x2 - 4 + sec -/R-4+2sec-1(즉)+c x2. +…

A: Integration

Q: 4-z² 2-y а zdxdydz = b Find a + b

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Q: Given the polar coordinates (1, - 4), which of the following would represent the p ㅇ(1, 쫄) O (1, 7)…

A: Given query is to find the equivalent positive angle coordinates.

Q: f (#) = 2x-3 and g () = ; then (f – g) (z) = %3D %3D Das- 9) (z) = 2 5 | b(f- 9) (x) = 2x2-3x-2 2x…

A: Given query is to find the value of indicated function.

Q: x²-4 dx can only be evaluated using trigonometric substitution technique . The True B False

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Q: 1 6. cos-xdx cos* xdx xprt.

A: We need to solve the integral.

Q: The New River Gorge Bridge is 880 feet above the water below. A bottle rocket is launched upward off…

A: To find out the velocity and acceleration.

Q: For the function, f(x) = 6x, determine whether it is one-to-one. If the function is one-to-one, find…

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Q: 2) Sx sin(2x?) dx 3) S cos?(2y) sin(2y) dy 4) f sec3 x tanx dx

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Q: Find the equation of the plane that passes through the point (2, 1, 1) and is tangent to the surface…

A: We have to find the equation of the tangent plane.

Q: a. f (x) sin x

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

Q: Determine whether the function is one-to-one. If it is, find a formula for its inverse. f(x) = x +7…

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Q: sin'x cosx dx Evaluate: (1- sinx)2(1+ sinx) 2 sinx sin 10x - +C 10 A) 8 (B None sin 10x +C 10 (D)…

A: ∫un du = un+1n+1 +C

Q: Find the critical points of the following function. 1 Inx f(x) =

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Q: Find the critical numbers of the function. y- 2 g(y) = %3D y2 - 2y + 4

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Q: Find the sum of the infinite geometric series 1 1 1 4 1 +.. 64 16

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Q: The marginal cost (in dollars per square foot) of installing x square feet of kitchen countertop is…

A: Here we will find asked quantities,

Q: The marginal revenue (in thousands of dollars) from the sale of x gadgets is given by the following…

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Q: Question 8 Evaluate: Jcos 2xdx cos³2x + cos2x A + C 2 cos³2x + C 6. cos2x B sin2x sin32x + C 6.…

A: topic - integration

Q: Graph f(x) = e +2. Choose the correct graph. OA. Ay 4- OB. Ay OD. Ay Oc. Ay o 包

A: We need to choose correct graph.

Q: sin2x cos3x dx= sin5xdx – sinxdx A True B) False

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Q: If  ?⃗×?⃗ = ⟨−3,5,−4⟩ and ?⃗⋅?⃗ = 4, find tan(?), where ? is the angle between ?⃗ and ?⃗.

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Q: Question 6 To begin evaluating sin*xcos°xdx conveniently, express: A sin'x as (sin²x)²and use the…

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Q: () If h(x) = | cosxdx and h =4, then h (0) is equal to 4 A -3 B 3 4 D -4 E) None C.

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Q: Determine whether the lines

A: To find out that the lines are parallel, intersecting or skew.

Q: 25— х2 -dx , if we let u=V 25 – x2 , then udu = – xdx. A True B) False

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Q: Let f(x) = -72* + 59a² + 201¤ + 143 be the function graphed here. Click on the graph and expand…

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Q: 1-coskx 2. lim kx = 0.

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Q: x*dx Using trigonometric substitution technique, | the simplified integral after substitution is: x²…

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Q: The x-intercepts of y = x2-4x-5 are: O a. (-5,0) and (1,0) O b. None O c. (-5,0) and (-1,0) O d.…

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Q: A Ferris wheel has a radius of 30 m, makes a full rotation in 3 minutes, and the axle stands 35 m…

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Q: dx , if we let u =V 25 – x² , then udu = - xdx. (A True B False

A: Given query is to find statement is true or false.

Q: 3. Evaluate the following integrals: cos e G = de J (1 + sin 8) vsin 0

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Q: Suppose that f and h are integrable and that: frx) = -1 , , f(x) dx = 5 , ,h (x) dx = 4 ,Find: a. -2…

A: We have to find the given integrals.

Q: Find the vertex of the parabola, y=x²+4x+1 O a. (2,13) O b. (-2,-3) O c. None O d. (-4,0)

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Q: Question 13 sin2x cos3x dx = sinSxdx - sinxdx A) True B False

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Q: Question 7 By algebraic substitution, the integral dx dx is converted to: 4+/x dy A) y+4 ydy B Jý+4…

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Q: 4. (i) Use the parametric equations of an ellipse, z = a cos (t) , y = bsin (t), 0 < t< 2r, to find…

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Q: x +1 8. J x(x+ 4)3 dx

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Q: Question 9 To evaluate J y-cse(y?)cor²(y³)dy, we let u =cse(y³) A) True B) False

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Q: 30+y 25+ 20 6, 18) 15+ 10 Find the area of the shaded region enclosed by f(x) = x3 + x2 - 6x and…

A: Explanation of the answer is as follows

Q: 9 Given that tan 0 and that angle 0 40 terminates in quadrant II, then what is the value of sin 0?

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Q: In’t dt 1. 2(9–In²t)' 4 tan e sec ede tan0-2 tan 0-15 2 2.

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Q: S. | sech (Insinx) cotxdx=2tan - (sinx) + C

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Q: Express f(x) in the form f(x) = (x-k)q(x) +r for the given value of k. f(x) = 3x +x + x-4, k= - 1…

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Q: 4V (7x – 5)5

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Q: 4tan e sec ede tan0-2 tan 0 –15

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Q: A function f has the form f(x) = a + b In(x). Find fif it is known that f(1) = 1 and f(2) = 8.…

A: Find your answer below

Q: 4. Show that if x, y, z are integers such that x2 + y2 + z? = 2xyz, then x = y = z = 0. (H)

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