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Q: Evaluate the following indefinite integrals. Show your solution. 1. f5 einx(sin x + cos x) dx ecos…

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Q: The area bounded by the graphs of y = 2 - x^2 and y = x^2 revolves about the x-axis. Determine the…

A: The given curves are y=2-x2 and y=x2   Now find the point of intersection between the given curves.…

Q: Scot³ x ( cz) ¹4 dx sec x tan x 5.

A: Follow the procedure given below.

Q: Find the lateral surface of the cone generated by revolving the line y = mx from x = 0 to x = 1…

A: Given

Q: Evaluate the multiple integral.* 22y [ ✓²)¢ dx dy 10 17.5 16.5 The area hounded by the graphs of y=

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Q: VI. Determine the instantaneous rate of change of the function √x sin (³) In 2 = = [X² f(x): dt 1 +…

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Q: Find the area of the region bounded by x = the horizontal strip. y²+1 and the y-axis using

A: Area between x=11+y2, x=0

Q: Test for exactness, then solve.  ey dx + (2y + xey) dy = 0

A: This question is related to differential equations, we will solve it using given information.

Q: 5. Use Cartesian coordinates to evaluate ㅋ yy dv where D is the tetrahedron in the first octant…

A: Let's evaluate given integral.

Q: (y² - x² sin xy) dy+ (cos xy - xy sin xy + e²x) dx = 0

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Q: Given the function f(x) √x f(x) = COS 2 1 + √r dr Determine the instantaneous rate of change at x =…

A: Using Leibniz rule of derivative

Q: Sketch the graph of r = 0 90° +2

A: To sketch the graph of r=θ90°+2.

Q: TU (sin³ x)√1 + cos x dx EN

A:

Q: The position of the sun at sunset, north or south of due west, depends on the latitude and the day…

A: We need to solve sinusoidal problem.

Q: II. Evaluate the following integrals. 2. (sin³x)√1 + cos x dx KIN k 플

A: Here is the solution:

Q: Jill burns 100 calories per hour while sleeping, 300 calories per hour while walking, and 200…

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Q: lim x++∞ x² + x e²x + In x

A: To Find: limx→∞x2+xe2x+lnx

Q: I. Evaluate the following limits 2. lim (3 + x)² x → +∞o

A: Given

Q: Find the are a of the region bounded by the given 1) sketch the area, ii) Determine the boundaries a…

A: This question can be solved using the concept of area under curves.

Q: -2 S₁² S₁² (²x²y^² + 2 (2x²y-² + 2y) dy dx 1 1

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Q: Evaluate the indefinite integral given below. Provide your answer below: f6e4 tan (2x) sec² (2x) dx…

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Q: Using the shell method, what will be the equation of the volume of the solid formed when the region…

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Q: So x² (a²-x²) ³¹/2² dx

A: A detailed solution is given below.

Q: 3. +∞ 8 -∞ dx x² + 1

A: Given ∫-∞∞dxx2+1To evaluate the integral:

Q: Find the area bounded by the curve y = coshx and the x- axis from x = 0 to x = 1. a. 11.75 sq. units…

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Q: A particle is moving along a horizontal line such that its velocity in m/s is given by v(t) = 2t²…

A: A particle is moving along a horizontal line such that its velocity in m/s is given by vt=2t2-16t+30…

Q: 5(-6)+(-4)(-1)/2^2-3+(-1)

A:

Q: Evaluate the integral: 9x - 5 S dx 9x² 18x + 13 —

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Q: | (sinh x)(coth’x + csch3x)

A: The solution is given in the next step.

Q: T Evaluate sec²20d0 a. 00.33 b. 0.5 c. 0.67 d. 0.25 e. NONE OF THE ABOVE O A OB O O D OE

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Q: Electric usage over the course of a day varies. The graph shown is of electricity costs per hour.…

A: Use average concept

Q: (13²-1| + |3²-3) da

A:

Q: Evaluate the following integrals 2x ·S- -dx 2 5+2x+x

A: We know that ∫duu = lnu+C ∫1v2+a2dv = 1a·tan-1va+C

Q: 2. Find the area of the region bounded by x=y², x=-1, y = 2 and y = -1.

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Q: If F(x) a. F'(1) L √4t - t² dt, evaluate the following: x² b. F(2), by interpreting F(2) as an area

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Q: Test for exactness then solve. (1 +  y2)dx + (x2y + y)dy = 0

A:

Q: 1. Let f(x) = sin²(x) cos(x) g(x) = sin² (x) cos² (x) h(x) = sin² (x) cos³ (x) ㅠ (a) Plot all three…

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…

Q: Find the value of the following definite integrals. Show your solution. 1. f(x¹+4) dx 2. (cos x +…

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Q: Perform the integration. TT 3 sec³x tan x dx 2 + sec x 0

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Q: 5x² S -dx 2. ex

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Q: Determine the order of the given differential equation and state whether the equation is linear or…

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Q: A small business determined that the price-demand and cost functions for producing and selling x…

A: We have to find the production for minimum average cost.

Q: Find the grea i) Sketch the ii) Determine the iii) vet up iv) Integrate 7) y=vin of the boundaries a…

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Q: Use the linear approximation to estimate In (√0.99).

A: Given problem:- Use the linear approximation to estimate In(3√0.99).

Q: 4. y = √esinx + 2 5. y = 4x In 4x 6. xe = sin 5x - sin 3y

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Q: 2. lim (tanx) (sin r-1) x→

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Q: P 2. ( a) Find the average value of f on [9,25]. b) Find all c in [9, 25] such that f(c) = favg.…

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Q: II. Evaluate the following integrals. fe (sin³x)√1 + cos x dx 2.

A: ∫π/2πsin3x1+cosxdx sin3x=sinx(sin2x)=sinx(1-cos2x) ∫π/2π(1-cos2x)(1+cosx)sinxdx let 1+cosx=t…

Q: velocity function of a particle moving along a horizontal line is given by v(t) = t² = 6t + 8, re t≥…

A: Please refer to the image below

Q: A solid consists of a right-circular cylinder and a hemisphere on each end. The length of the…

A: The diagram of the cylinder with hemisphere on the end will be as following To find dVdr at r=2,…