Arcsin(x/y) = 4x + 3y

Q: ydy (1+ у)*

A: We have to find the integral.

Q: Exercise 1. Find the following limits 2 3x + tan 2x 2x + x tan 2x sin 1) lim 2) lim 5x +x tan 2x 3)…

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Q: The traffic flow rate (cars per hour) across an intersection is r(t) = 500 + 600t – 120t2, where t…

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Q: Problem 5 Solve (y')? + 2 y' – 3

A: We need to solve D.E.

Q: 6. Evaluate f z z* –8 dz. A) (x² - 8) +C B) a O b O d

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Q: Find maclurine seris sin

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Q: park ranger at point A observes a fire and estimates the angle of elevation to be 25 degrees.…

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Q: Researchers found the demand for cheese in a particular country for a particular year can be…

A: The equation is given by lnq = D-1.32lnp                                 ........1 Where, p…

Q: 2x2 ) 3x Evaluate the given limit of lim if it exists. 1 x +1 O 1 O limit does not exist 2

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Q: Solve the problem and give a detailed solution. Find the 3rd derivative of y = ln(cos(e3x))

A: Note ÷ I have used chain rule and product rule multiple times. Please look carefully.

Q: Problem #2: Differentiate f(x) = [(4x³ – 1)(8x² + 6x – 3)]° and solve f'(2). %3D Solution: Reason:

A: To differentiate the given function.

Q: ne area A of a circle is increasing at a rate of 167 cm² /s. Find the rate of ne radius r of a…

A: We have to find change in radius

Q: 1. Algebra: Compile 1 application problem for introduction to algebra with solutions and correct…

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Q: dx S. 2x - 1 e

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Q: 3 cSC x cot x dx

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Q: 4. Evaluate (10** dx. 1000* 10 -10* +C A) +C In10 In10 10 100 B) 10* +C D) 10* +C In1 In10

A: We can find the integration as below.

Q: Sx² sec2 x³ dx

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Q: arctan x dx

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Q: The following series is divergent: n5-2 Σ 5n4 n =1 Select one: O True O False

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Q: Given the function y = x3 - 5x2 - 8x + 3. Determine the following: a. maximum point b. minimum point…

A: The given function,  y=x3-5x2-8x+3

Q: Differentiate the following function. r(1) = (e!2e!-4e) %3D r(1)=

A: We can solve as follows

Q: Problem 4 Solve x Iпy lnx dy + dx

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Q: 1 ): The vectors 2 and form a basis the vector space R'. Select one: O True O False

A: Here we state whether it is true or false.

Q: 4. If the characteristic equation of the differential equation y"+2y'-3y =0 is m² + 2m –3 =0, then…

A:

Q: A. Evaluate the following integrals. 1. S(Vcos x + sin x)´dx 2. S cos³ 3x dx 3. S tan5 2x dx

A: To evaluate the following integrals.1 ∫cos x+sin x2 dx2 ∫cos33x dx3 ∫tan52x dx

Q: The average rate of change of y with respect to x over the interval [0, 3] for the function y = 3x…

A: The function y=3x+2 over the interval 0,3

Q: x2-4 dx S xVx2-9

A: solution:-∫x2-4xx2-9dx=∫xx2-9dx-∫4xx2-9dx                            =12∫2xx2-9dx-4∫1xx2-32dx…

Q: 1. (a.) Name the given quadric surface and give its axis. (b.) Sketch the surface. (c.) Name its…

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Q: 10. S V9x2 + 64 11. ( sech?(In x) 12. S cosh(5x – 7) dx

A: Given

Q: csc(cot x) + cos? x dx .2 sin“ x

A: The given problem is solved below in detail.

Q: Find the volume of the solid obtained by rotating about the x-axis and the region bounded between: y…

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Q: Evaluate d:/dx on the surface x: + + x²y®=² = 3 at the point (1, 1, 1).

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Q: : Solution of ydx – xdy + (1+ x2)dx + x2sinydy = 0 is

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Q: Express à = (3, 1, –1) as B + Č, where B is parallel to the vector (1, 4, 2) and Č is perpendicular…

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Q: 4In(Arctan x) = 1-y

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Q: . Evaluate cos 0 if sin 0 = -1/4 and 0 is in quadrant II

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Q: Find the Jacobian of the transformation. x = 6u/v,    y = 7v/w,    z = 4w/u ∂(x, y, z) ∂(u, v, w) =

A: To find the Jacobian ∂x, y, z∂u, v, w of the following transformation.x=6uv, y=7vw, z=4wu

Q: 5. If the characteristic equation of the differential equation 27 - 184 dx +8- y-0 is dx 27m -18m…

A: The characteristic equation of the given differential equation is 27m4-18m2+8m-1=0.

Q: Sx In x dx

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Q: Find the linearization L(x, y) of the f(x, y) = x°y® at the point (2, 2). L(x, y) = %3D

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Q: If a series Σ an n=1 is convergent, then it is absolutely convergent.

A: 1)∑n=1∞ an is convergent,then the series may not be convergent.for example, an is alernating…

Q: S csc6 3x dx 9° S cot5 x dx dx cos* 6x

A: We know that csc2θ - cot2θ = 1 sec2θ - tan2θ = 1

Q: f (x) +f (1 – 4 ) = x

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Q: a2– x2 (x+y)dæ dy

A:

Q: Which of the following is NOT a differential equation? Select one: x + 2y" = 3 O None. O 2xy' = 3 O…

A: The given problem is solved below.

Q: 6.) What is the derivative of f(x) = x| at x= 07 a.) r'(x) = 1 c.) f'(x) = 0 b.) f'(x) is undefined…

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Q: If f(x) = 7 tan-(2 sin(4)), f'(2) =|

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Q: Find the equation of the tangent line at the given value of x on the curve. 3 4 2y° + xy - y =…

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Q: Evaluate the following. Give an exact answer, not a decimal approximation (a) csc 2 (b) sec (c) cos

A: Topic:- trigonometry ratios

Q: Use a right triangle to write the expression as an algebraic expression. Assume that x is positive…

A: see below the answer and calculation