Hello, Please show all your and solve the following the

Q: Solve the initial value problem. dy 27) dx = x(6+x²)²₁ y(0) = 0

A: Given query is to solve the differential equation.

Q: In the related rates problems, what variable are we differentiating each function with respect to? O…

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Q: Find the equation of the parabola described below. Find the two points that define the latus rectum,…

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Q: 3 Given [ (x³ - 3x²¹ + (x5 - 3x4 + 6x³ + 3)dx, evaluate the indefinite integral.

A: We have to solve given Questions.

Q: 7x+2 8- Find S dx (Using substitution method). √7x-3

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Q: m(x)=ln(4-x^2) Find domain

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Q: 4- Find the volume of the solid obtained by rotating about the x-axis the region under the curve…

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Q: Given the sequence an This sequence is bounded This sequence is monotonic This sequence diverges sin…

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Q: For the equation given below, evaluate y' at the point (2, –1). y'at (2, -1) = e³ + 10 − e¯¹ = 2x² +…

A: To find derivative of the given function.

Q: a) Evaluate the following integral. 2 2w5-3w+8 dw 2w² S²

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

Q: -X. cos(2x); dy = ? е 17) y = e

A: Given function  y=e-xcos2x

Q: Find the minimum and maximum values of z= 5x + 6y, if possible, for the following set of constr…

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Q: Find • JJS ₁² z dV, where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), (0,2,0), and…

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Q: Calculate the derivative of: f'(x) = sec² (15x) f(x) = COS -¹(15x) sin ¹(15x)

A: Given function:- fx=cos-115xsin-115x

Q: Consider the given differntial equation y'(t)= (y-2)(3+y) Find the soultions that are constant for…

A: Given: y'(t)= (y-2)(3+y)

Q: The angle addition formula for sine is sin(a ± ß) = sin a cos ß ± cos a sin ß. Use this formula to…

A: We have to solve given Questions.

Q: 1. An airplane heads due north at 280 mph. It experiences a 38 mph crosswind flowing in the…

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Q: Thanks

A: We have to find the value of the given following conditions according to the given information

Q: Convert from rectangular to polar coordinates: Note: Choose r and such that is nonnegative and 0 ≤ 0…

A: The given points are, a) 6, 0 b) 3, 33 c) -2, 2 d) -3, 1 We have to convert these points into polar…

Q: Cumulative world production of solar cells for generating electricity is predicted to be 58e0.43t…

A: According to question,Given Function,y = 58 e0.43 t

Q: 6- Find the volume of a solid, use the Cylindrical Shells method, which involves rotating the region…

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Q: In z [122 10. -da dx

A: NOTE: Refresh your page if you can't see any equations. . use the integration-by-parts method…

Q: 2 (b) ₁² ( + 6x) dx X

A: ∫xndx=xn+1n+1+c∫14(2x+6x)dx=2∫141xdx+6∫14xdx

Q: f f(x) = V x + 1 , for x 2 -1, then for y 2 -1, fy2 + 2 y ) y + V2x+ 1 ) 1 - وكاد 1 ) V2x+y2

A: f(x)=x+1for f(y2+2y)  put x=y2+2y in f(x)

Q: Find an equation of the tangent line to the curve x = √√t, y=t² - 2t at the point corresponding to t…

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Q: 2- Find the equation of the tangent line to the curve 9xCos(7y) + 5y = 9 at y = 0.

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Q: 3- a) Find the area of the region in the first quadrant between, y || = and y = x² b) Find the…

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Q: 3. Find the inverse function f-¹(x) of f(x)=3 sin 2x

A: The given function is: fx=3sin2x   To calculate the inverse function of the given function…

Q: If the function f(x) has the graph pictured below, then: a) f(x) 0, whenever 5 f(5) e) f(6) > f(8)

A: Given: Graph of function f(x) -

Q: cost of maintaining a home generally increases as the home becomes older. Suppose that the…

A: Given query is to find the formula for total cost and the cost for 4 years.

Q: 1. Express in the form y = f(x) by eliminating the parameter. x = e-³t; y = e6t

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Q: Find the average rate of change of the function over the given interval. 1) y = √√√2x, [2, 8]

A: formula for average rate of change is  =f(b)-f(a)b-agiven f(x)=2x , given interval is  2,8there for…

Q: (x)=(3x2−12)2 Step 1 of 2: Find the second derivative of the given function.

A: dxndx=nxn-1d(constant)dx=0

Q: 6. Consider the function f(x) = e¹/x. (a) What is the domain of f(x)? (b) Find all vertical…

A: By drawing a graph of y=e^1/x  We can clearly see

Q: Use implicit differentiation to find dy/dx. 14) xy + x = 2

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Q: ), find

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Q: The function s = f(t) gives the position of a body moving on a coordinate line, with s in meters and…

A: dtndt=ntn-1formula is speed =dsdtaccelaration=d2sdt2

Q: Particle P moves along the y-axis so that its position at time t is given by y(t) = 4t²5t + 7 for…

A: Given, Position of the particle P is given by yt=4t2-5t+7 The position of the particle Q is given by…

Q: tangent lines?

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Q: 36 identical tasks are distributed to 9 different people. Each task is assigned to exactly one…

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Q: Calculate ff f(x, y, z) dS For Part of the surface x Js f(x, y, z) ds = S - z³, where 0 ≤ x, y ≤…

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Q: question 30 Find the area enclosed by the curves f(x) = 37 - x^2 and g(x) = x^2 The area (rounded…

A: Given functions fx=37-x2,gx=x2

Q: 9- a) Evaluate the following integral. b) Find the indefinite integral: S c2 2w5-3w+8 dw S² 2w²…

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Q: Question 2. Find the volume of the solid obtained by rotating the region bounded by 9x² + 4y² = 36…

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Q: Determine the limit by sketching an appropriate graph. for x

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Q: ²4 cos 20; (0, ± ; (0, 4)

A: We have to find the value of the slope of the tangent of the above polar equation.

Q: Question 22 Find the average value of f(x) = 8x - 4 from 1 to 5. The average value of f(x) = 8x -…

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Q: weekly price-demand and cost equations are, respectively, p=487 -0.37 x and C(x) = 20,127 +22 x.…

A: Given price demand function p = 487 - 0.37x Cost function C( x ) = 20127 + 22x as we know that…

Q: The value of 5 1 x² [³ - dx is

A: Given query is to find the value of integral.

Q: What is the are between the graph of y=4x³+2 and the x-axis from x=1 to x=2

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