Let R be the region bounded by the graphs of y = r-1, y = 1-2³ and the lines y = 3 and r= -1 as shown below.

Q: Using Wallis formula, find the integral of the expression. Answer in 5 decimal places (example…

A: We will use Wallis integral formula to solve this question.

Q: Use the graph of g(x) to answer each question. (a) Find the domain and range of g(x). Write the…

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Q: Evaluate: lim (1+sin 4x)cot ¤ x→0+

A: Topic:- limit calculus

Q: Let L(c) be the length of the parabola f(x)=x² from x = 0 to x=c, where c20 is a constant. a. Find…

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Q: I > | − 4 • xª + 5ª

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

Q: af Find and ?x af Əx af || - for the following function. dy f(x,y) = (x³ -1) (7y + 9)

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Q: Consider the following sequence defined by a recurrence relation. Use a calculator, analytical…

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Q: Find all the second-order partial derivatives of the following function. h(x.y) = 2x e +y +4

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Q: rcosh z Let F(x)= 1. Find F(0). 2. Find F'(x). √√√x+1 sin(1 t) dt.

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Q: Identify the definite integral that computes the volume of the solid generated by revolving the…

A: Question- Identify the definite integral that computes the volume of the solid generated by…

Q: Use the method of cylinders to determine the volume of the solid obtained by rotating the region…

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Q: A car leaves leaves the sa the first car at that insta

A: Here we have to find the rate at which the distance between the two cars is changing.

Q: p(5y-4) dy y³+ 4y²

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Q: Completely factor and find the zeros of the function (x)=6x¹-11x³-51x² +99x - 27 Describe the…

A: To find the factors and zeros of the function.

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of y=2x + 1 and…

A: find intersection

Q: For the function (a) Find the domain of g(x). (b) Simplify g(x). (c) Find any discontinuities in the…

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Q: Use the line sketch tool to draw the horizontal and T vertical components of this vector. Write this…

A: Sketch of given vector,

Q: Let f(x) = (lnx)7 f’(x) = ƒ' (e¹) =

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Q: Match each function with its derivative. Y • x² x4 + 5x 1. cos x - - x8 8. sin x + x4 3x x4 -1.…

A: Concept: Differentiation of xm dydx=xm=mxm-1 dydx=ax=loge(a)· ax

Q: A balloon is release from the ground 200m from an observer. The balloon rises 42 directly upward at…

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Q: 5元 3) 3 S元 6. 0- 7元 11元 6. 6. 4元 3 元一6 3. R一3 2. 如一2 R一2 3. 与一3

A: Given polar coordinate is 2,5π3. Choose the circle with radius 2 and then the given angle.  The blue…

Q: Find the volume of the solid generated by revolving the shaded region about the y-axis. The volume…

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Q: Find the volume of the solid generated when one arch of the curve y = sin x, from x = 0 to x = π, is…

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Q: The length of a rectangle is given by 4t 3 and its height is √2t, where t is time in seconds and the…

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Q: Show that the following series diverges. Which condition of the Alternating Series Test is not…

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Q: Approximate the sum of the series by using the first six terms. (See Example 4. Round your answer to…

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Q: Using Cramer's rule to solve the following system of equations, what D, D, D and D₂? are 4x + 3y +…

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Q: A fencing is limited to 50m length. What is the maximum rectangular area that can be fenced in using…

A: Recall:  Area of rectangle=length*breadth

Q: Find the area of the region that lies indie the circle r = 3 sin 0 and outside the cardioid r = 1 +…

A: Concept: Cardioid: A cardioid is a geometric figure with a heart configuration. It is the location…

Q: er the questions below: I z²,e²,4x³z + ye² COS Z > done by F in moving a particle along the cur π Ả…

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

Q: Solve the system of differential equations. 0 x' = - [8 %] = 0-5 x₁(0) = 8, x₂(0) = = 15 x₁ (t) = X1…

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Q: Determine whether Rolle's Theorem can be applied to fon the closed interval [a, b). (Select all that…

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Q: Evaluate the integral: –(9z²+7x) dr %3D (1-1)(z+1)²

A: Given :∫-(9x2+7x)(x-1)(x+1)2dx

Q: 218x- 2y-z= 10 x-3z = -2 3-x+y-3z=-4 |

A: We will solve this system of equations algebraically.

Q: Evaluate the following integral, or state that it diverges. S8x² e-x³ dx Select the correct choice…

A: We have to find integral

Q: Dot Products Dot Angle Between The dot product of two vectors is u · v = uqV1+U2V2 Vectors Correct?…

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Q: Find f, f, f. fx= f(x,y,z)=x-√√√²+z² (Type an exact answer, using radicals as needed.)

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Q: Find fx, fy, f₂. fx = f(x,y,z)=x-√√√²+z² (Type an exact answer, using radicals as needed.)

A: topic- partial differentiation

Q: It takes 1100 J of work to stretch a spring from its natural length of 1 m to a length of 2 m. Find…

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Q: Solve the problem with the application of integral and draw the complete figure of the problem.…

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Q: -5x+ y=-3 3x-8y 24

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Q: 'SC x x x

A: ∫cot2(x)csc3(x) dxWe know that cot2(x)=csc2(x)-1=∫csc3(x)(csc2(x)-1)dx=∫(csc5(x)-csc3(x))dxWe know…

Q: Identify the type of quadric surface defined by the equation 0, 2 4 and find all x-, y-, and…

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Q: Differentiate with respect to x y = e" cos(x²) e* (cos(x*) – 2x sin(x²)) e* cos(x²) – 2x sin(x²)…

A: y =excos(x2) dy/dx = excos(x2) -2xexsin(x2)           =ex(cos(x2) -2xsin(x2)) option 2 is right…

Q: Find the area of the surface generated by revolving the given curve about the x- axis. y=6x, 0≤x≤ 3…

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Q: Use logarithmic differentiation to find dy/dx. y = (6 + x)x, x > 0 dy dx

A: This question is based on product rule diffrentiation and log properties.

Q: Use the Rational Zeros Theorem to find all the zeros of P(x) = 2x4 + 5x³ − 3x² − 15x – 9.

A: We have to find out the zeros

Q: 3. If Ax) = , find f"(-1). c. 0 d. -1 a. e b. 2e

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Q: Suppose that you have the utility function: u (x) = Vx u" (x) 43 %3D Find : u' (x) 1 2x 2x Option 2…

A: I have stated the used formulas in the solution

Q: A product is introduced to the market. The weekly profit (in dollars) of that product decays…

A: topic -rate of change of a function