In Exercises 1 through 4, find the area of the shaded region. 1. y= Vx

Q: 5- y? = 4x (4, 4) y = 2x – 4 (1,-2) Using a horizontal element of area, the area of the shaded…

A: Here  we have to find the area of shaded region.

Q: Explain why the function f(x) = ez is not injective (one-to-one) on its natural domain.

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

Q: dy Use implicit differentiation to find dx 2x - 5 3y? 2x +5 dy dx

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Q: Stan@ -1}de

A: ∫ tanθ dθ = -lncosθ+C ∫sec2θ dθ = tan θ +C.

Q: y cos x+sin y+y 0. Solve the following dx sin x+x cos y+x differntail equation 1.

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Q: 21. Write the definite integral that repre formed by y = x² + 2x + 1 and y=2x+5. Do:

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Q: Find the general solution of the given ODE x +1 y': y* +1 x? + r- - y? = x +4x + k Option 1 O Option…

A: integration

Q: dx 2. To evaluate | by trigonometric substitution, we let (5 – 4x – x - A. x+2= 3tane B. x+2= 3sine…

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Q: 13. Eliminate the parameter t, sketch the curve, and indicate the orientation. x=5 sint, y= 5cost,

A: We will square the both equations and then we will add them to eliminate the t

Q: f (x)= arcsin (x³)+ aretan (4x)

A: derivative

Q: 2x+5 Зх +1 5) lim 2х+5

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Q: Let F(x) = f(æ*) and G(x) = (f(x))*. You also know that a' = 3, f(a) = 2, f'(a) = 8, ƒ'(a*) Then…

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Q: The differential equation (x²y-2x- 3)dx+ 2dy=0 O Linear in y Linear in x O Homogenous O Exact

A: Given a differential equation

Q: Part 4: Solve the following problem. Show your complete solution. 1.) Find the equation of the…

A: A detailed solution is given below.

Q: What is the solution of D.E y" – 2y' = e*sinx when solved using the method of undetermined…

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Q: Use the properties of the derivative to find the following. r(t) = ti + 5tj + t?k, u(t) = 5ti + t?j…

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Q: Solve the equation (y - (cos x)^2)dx + (cos x) dy = 0

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Q: Solve using product rule d(uv) = u dv + v du: f(x) = (x^2 + 4) (x^4 – 4x^2 + 16)

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Q: 1. Calculate the area of the graph enclosed by the curve y = sec(2x)tan (2x), the x-axis, and the…

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Q: 8. Use vectors u = -3i - 3j, v = -li, and w = 5i + 6j %3D a. Determine the angle between u and w. a.…

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Q: Use the graph shown to determine if the limit exists. If it does, find its value. lim f(x) X-1…

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Q: Use the graph of y fx) shown at right to find the domain of f. 345) (-63) 9,3) The domain of fisO…

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Q: Find the equation of the tangent line at the given point on the curve. xy? = 36. (1,6) The equation…

A: This question is related to equation of straight line, we will solve it using given information.

Q: 1. A soccer ball is kicked with a speed of 75 mph at an angle of 30° from the horizontal. Write the…

A: Given query is to find the velocity components.

Q: sech2(In x)

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Q: P7: x3 + x – 1 x(x – 1)(x + 5)²

A: The given problem is solved below in detail.

Q: convergent or divergent. Please provide detailed solution. a) : E 10" n=1 (n + 1) 52n + 1 00 -5n 2n…

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Q: is a function of K, and y, and tan - z*e®Y.

A: Given problem:- Z is a function of x and y tan√(y2+x2) =zx e6y  To find:-

Q: Find the angle of the largest right circular cone which can be inscribed in a sphere of radius 9…

A: We have to find the angle of the largest right circular cone which can be inscribed in a sphere of…

Q: Show all necessary solutions. I. Find the equations of the horizontal and vertical Tangents. a. 25x?…

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Q: Find and b such that the following function is continuous at x=( [x] – 2a x 0 -

A: To find the values of a and b

Q: Evaluate the integral -2x + 4 dx J (x² + 1)(x – 1) 2

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Q: Find the surface area of the plane ( 15x- 5z+20y=35) if it is in the first octant

A: Given problem:-   Find the surface area of the plane ( 15x 5z+20y=35) if it is in the first octant

Q: (1- sin@) ) (1-sini (It sine

A: Given: I=∫dθ1-sinθ1+sinθ   As we know that; The trigonometric identity: 1). sin2x+cos2x=1 2).…

Q: 9x2 dx Vx3+2

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Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the…

Q: Which of the system of equation has no solution? 2х - 4y%3D 4 – 3x + 6y = – 9 а. С. X— 2у %3D 3 | 3x…

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Q: y = sinx dy V1+x? sin dy V1+x sinx+x x+x (sin" x)' Jī- dx (sin" x) Vi+x² dx Op tion 2 Option 1 V1-x…

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Q: Solve the second derivative(y") of the following

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Q: P2: |(e* sin x + x In x) dx

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Q: I. Show that the function f defined by (1, y) = (0,0) %3D f(r, y) = (1, y) # (0,0) I+ y is not…

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Q: Find the equation of the tangent line at the given point on the curve. 2y - Vx = 4. (16,2) y =U

A: We need to find equation of tangent line.

Q: I need the graph of the solution and describe its behavior as t increases

A: Apologies for the inconvenience. The solution is: yt=-1+5t3e-13t [used t place of x in the original…

Q: Find dy for the given values of x and Ax. y = 5x° - 9x, x= - 2 and Ax= 0.2 dy =D %3D (Round to the…

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Q: sove the fowowing, using Lagrange Multipiiers: Maximize flR, Y. 2) solaject to x2 + Ax + a4 t 2 + 2…

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Q: Use the properties of the derivative to find the following. r(t) = ti + 5tj + t²k, u(t) = 5ti + tj +…

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Q: L x² cos 2x³ dx? After substitution is performed, which of the following is equivalent to

A: Given that the integrals  To find the evaluate and choose the correct answer

Q: 2. A 15-meter-long ladder is leaning against a wall The bottom of the ladder is pushed horizontally…

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Q: Find the surface area of the plane ( 15x- 5z+20y=35) if it is in the first octant

A: Here we have to find the surface area of a plane.

Q: EXERCISES Solve the following differential cquations 1. =-sec(xy) Ans. sin x = +C dx 2x2 x +y Ans.…

A: As per our guidelines we can help you in solving only first problem rest of the problems you have to…