Find sin (θ) given that cos (θ) = 1/5 and θ is in quadrant IV.

Q: Ex. (9) Sol:- Solve 3y"-2y'+y= 4x+2

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Q: e²+2y + sech T = cot y + log2 (tanh x)

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: II. Find Do not simplify your answers. da 1. log, (√2x² + y) + tan(x² − ³) = sin¯¹ (2² − 1) + 2

A: log3(2x23+y )+tan(xπ-πy)= sin-1(x2-1)+π21log(3). 2x23+y 23×23x-13+y'+sec2(xπ-πy).(πxπ-1-πy.…

Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 3. lim (x-3) tan(9-x²)…

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 1 + ²/ 1. lim x12x² + x1

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Q: Find the horizontal asymptote of f(x) = y = 5x + 2x³ +3 5x³x2-4

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Q: -2/√√/3 dx x√√x²-1 • [²/²2 (x + 12/²3). dx sin² π/6 28. • √2 30.

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Q: 3. S 2 x²+a² x4 = _ (x² + a²) ³² 3a²x3 -dx = + c

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Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: We have to integrate the given function for the given limits

Q: 1. f/² sin (1) cos (4) Sir sin (²) dx (Consider initially the first 2 terms)

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Q: du du

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Q: Using trigonometric substitution to solve: f 1 A + C 8 sec x√4-sin2x sin 2x + C 4 cos x√4-sin²x sin…

A: Solution is given below:

Q: fe²x+Inx² sin x² dx = e2x cos x² dx

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Q: Solve the differential equation and simplify (D^3 + D)^2y = 0

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Q: /² sin ( cos() sin() dx (Consider initially the first 2 terms)

A: To evaluate the value of given integral.

Q: 6x5-25x+8x3+43x²-8x-12 4. Find (3x+-11x² +9x²-11x+6) (9x²+12x+16) -dx if this can be reduced to 63…

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Q: Given: (1+2x) e-x dx. Using integration by parts and letting u = -1- 2x, dv = f(x)dx, then the value…

A: Let's find.

Q: y = 2 x + 2 -3+x

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Q: Integrating Factor by Linear Equations: 9. +xcoty ecosy =

A: Given that a differential equations and we solve this differential equation by using integrating…

Q: A continuous O Ext F(XI = Find ***** V-V- K x has CDF X Co oxx cl 15X value of k 16 17 18 19 20 21…

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Q: VI. Write TRUE if the statement is correct, otherwise write FALSE. There is no need to justify your…

A: 1. True 2. True

Q: u be a differentiable function of du (a) (er) dr d du (b) = (6") = b. Inb dr dr 1 du (c) (In u) dx u…

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Q: d d Calculate[r₁(t) r₂(t)] and [r₁(t) × r2(t)] first by differentiating dt the product directly and…

A: This question can be solved using the concept of dot and cross product of two vectors and…

Q: If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D are constants, ....…

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Q: Question 7. A manufacturer of jet engines estimates that the rate at which maintainance costs are…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 4 Identify the center of the conic section whose equation is x 2 +y 2 + 6x - 4y - 12 = 0. (-6, 4)…

A: The given equation is; x2+y2+6x-4y-12=0   As we know that; The general form of equation of the…

Q: A continuous F(x1= 글X K value V-V- 15 X x has CDF 16 X Co OBX C1 15X k of 17 18 19 20 21 An

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Q: II. Find dz Do not simplify your answers. 1. log,(√2x² + y) + tan(x − ³) = sin¹(x² - 1) +

A: We can solve this as follows:

Q: +x+1 2x² +2+x³+x dx = [Aƒ'(x) − B ln(g(x)] + D, and if A=B<0, then f x+2 -2x + +5In(x + 2) + C 2 x²…

A: Solution of the problem as follows

Q: Question 7 Given : A B E 0 2π 3 F|+ π 4 (U) =|m x³sin(2x) dx = 3 5π 6 3πt 4 277²-24 64 Find bif sbst

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

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Q: . Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 4 4. lim loga (x+3)…

A: limx→1-log12(x+3)1-cosh(cos-1x)=limx→1- log2-1(x+3)1-cosh(cos-1x)since, limx→af(x). g(x)=limx→a f(x)…

Q: 8 Given: (В © √³x³sin(2x)dx= F4 5T 6 21 Зд TL 277²-24 64 T Find bif sb st

A: Solution is given below:

Q: Write an equation for a function that has a graph with the given characteristics. The shape of y =…

A: We can find the correct answer as below.

Q: II. Determine if [x+1]. if x < -1 S x + 1 f(x) = 2 tanh (x+¹) if 1<x< 1 1-x In [cosh (x + 1) + sinh…

A: It is solved whether f(x) is continuous or not.

Q: Bernoulli Equations: 1. (x² + y²)dx - xydy = 0

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Q: Using trigonometric substitution to solve: sin 2x + C 8 cos x√3-cos²x sin 2x 4 cos x√4-sin²x secx 8…

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 2. lim (√²-x- (x² + x)

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the area under the curve y = Find the average value of y = 7x³ over the interval [0, 4]. 7x³…

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Q: Calculateri(t) r2(t)] and r₁(t) x r2(t)] first by differentiating dt the product directly and then…

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Q: Question 1 sec42x Find -dx tanº2x -=(corº2x) ( 11 12 tan62x cot22x- - (cort2x) A - 1/1 (0 (A) B…

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Q: 2x2 40. Determine which of the following is the integral off 5 cos x dx. a. -5 sin x + C c.cosx+C b.…

A: To evaluate the values of given integrals.

Q: Integrating Factor by Linear Equations: 7.xx-y-5x43x² + 2x = 0 dx

A: Let's find.

Q: orrect. a k(t) ||r' (t) × r"(t)|| ||r' (t)||³ = r(t) = e¹0ti + e-tj tc

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Q: x² dx (x²+4)5/2 Sπ/4. (Use trigonometric substitution)

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Q: π/4 ²dx (x²+4)5/2 (Use trigonometric substitution)

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Q: Question 5 A) O B) 48 32 D) 96 If f cos+2t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A,…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Consider using the method of partial fractions to solve dx x²+x+1 2x²+2+x³+x - dx = [Aƒ (x) − B…

A: Given problem:-

Q: II. Find Do not simplify your answers. 1. log, (2x² + y) + tan(x − ³) = sin−¹(x² − 1) +

A: Given problem:-