9. (Trigonometric Substitution) Let x = 2 sin(0) for 0 < 0 < . Write v4 – x2 as a trigonometric function of 0.

Q: тх e COs nx dx

A: We have to evaluate the integral  ∫emx cos nx dx.

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Q: %234 #4 Detelmine whe ther the sories Ć 4"-3 4^_3^ converges or diverges. If it converges find its…

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Q: Let f(x, y) = 2x2y + 3xy. Use the (limit) definition of partials derivatives to show that fx(x, y) =…

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

Q: 5. (4x3 — 6ху?) dx + (4y3 — 6ху) dy 3D 0

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Q: Solve using trigo substitution

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A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

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Q: Evaluate the integral (Trigonometric Substitution) |(a?x* – x®)&dx 6. x³)Zdx

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Q: Let f(x) = 4x^2 – 7x. Use the ɛ/ō-definition of the derivative to prove that f(2) = 9.

A: Given

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A: We have been provided with 10 points in a plane such that no three points are collinear.We need to…

Q: 12sin3xcos7x dx

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Q: Assume the acceleration of the object is att)--9.8 meters per second. (Neçlect air resistance.) With…

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Q: 21. A group of 10 women and 6 men must select a four-person committee. How many committees are…

A: Let's find.

Q: Consider the following series. 8 + e-n n = 1 What does the Test for Divergence reveal about this…

A: We know the necessary condition for the convergence of a series. A series ∑nan   is convergent…

Q: -2V-6 6. The gradient of a curve is given by = 3). find the equation of the curve. Given that the…

A: Equation

Q: 8. Find i • i 55° lū| = 7| = 31

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A: The given curve,   y=x33+14x, 1≤x≤2

Q: aluate the integral sin³ .2 x + cos² x + 1 dx sin? x (cos? x + 1)

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Q: 12. Given f (x) = x³ – 12x + 1 (a) Find the intervals on which f(x) is increasing or decreasing. (b)…

A: I have appended the formula used in the solution part.

Q: If f(x)=-(x² – 4), find (a) The x-intercept and the y-intercept (b) The interval where the function…

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Q: Draw the graph, identify the region, and sketch the representative rectangle. Label the graph…

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Q: f(x) f'lx) %3D

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Q: 3. Anabelle would like to invite 9 friends to go on a trip but has room for only 5 of them. In how…

A: We can solve this as follows:

Q: 1 7. (x dy – y dx) = 0 x² + y?

A: We are given a differential equation  1/(x2+y2) ×(xdy - ydx ) =0 We have to determine whether it is…

Q: V 2 y = 3 Vx

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Show that (xcos(2x)dx=. A-2 8

A: LetI=∫0π4xcos2xdxPut 2x=udifferentiate on both side2dx=dudx=du2As x→0 then u→0As x→π4 then…

Q: Calculate

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Q: Jse one of the formulas below to find the area under one arch of the cycloid x = t – sin(t), y = 1 –…

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Q: Suppose an object moves along a line at 19 m/s for 0sts2 s and at 25 m/s for 2<ts5 s. Sketch the…

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Q: 3. y = Vĩ,0< xs1

A: Apply formula for surface of revolution

Q: | 3t³ (t² + 4)5dt

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Q: Is 3 A m, m being any real number, possible? Explain. [IC]

A: This is a problem related to vector parts. Based on the general formula and concepts we will answer…

Q: 10. Given i [10,4] and [12, – 13], find the projection of i on

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Q: Prove the given identity. tan0 + cot0 = csc@sec®

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Q: it is always that when the series equal to zero it converges and when it is nonzero it diverges ?

A: For a series to be convergent we must have limn→∞an=0. But the converse is not true.  For example:…

Q: Evaluate the integral (Partial Fraction Decomposition) xdx J (x² + 2)(x² + 1)2

A: ∫xdx(x2+2)(x2+1)2Substitute u=x22→dudx=x→dx=1xdu=12∫1(u+1)(2u+1)2duPerform partial fraction…

Q: Evaluate the following integrals? .3 1)S x² e3* dx 2) S dx x²+25 dx 3) 6x – x2 4) | cos(In x) dx

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: tan x If f(x) = 3 sec a f (2) = f (1) =

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Q: Sketch the graph of the following equation 2x + 6y + 3z = 12

A: To sketch the graph of given equation

Q: 4. An earth satellite moves in a path that can be described by x2 72.5 = 1 71.5 where x and y are in…

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Q: 14 of 19 Which of the following is a parameterization of the line that passes through the point (1,…

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Q: Direction: Find the equation of the tangent lines. Show your solution. 1. f(x)= x2 +5x + 1 at (6,…

A: As per our guidelines we are supposed to answer only one question at a time. So I am solving the…

Q: 5. Given R(t)= 2 sin ti+5 cos tj+tk. Find T (t) and N(t) of the mov by the given vector.

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Q: 1.) Determine the largest interval over which the function flx) = \x+3 is continuous. 2x 2.)…

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