156. Find the area of the region D, bounded by y = √4x², x= √3, which is the region x=2, and y = 0.

Q: Compute[x² sin(2x)dx. A.- x² cos(2x)+ xsin(2x)+ cos(2x)+C 1 1 B. — — x² cos(2x)+ —…

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Q: Consider the position function s(t) = -4.9t +31t+24. Complete the following table with the…

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Q: For which of the following integrals should substitution be used, instead of Integration by Parts?…

A: Solution :option D substituition be…

Q: A B D 0 Consider the integral f sin ¹x dx. If we let u = sin ¹x and dv = dx, the integral can be…

A: We have to above question

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Q: Solve ₂(x + 1)(x + 2)²(x²-1)dx with and without the even-odd theorems (show both solutions).

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Q: Solve the differential equation a. (4x³y² - 6x³y - 2x - 3)dx + (2x¹y-2x³)dy=0 b. (x-4y-3)…

A: If the differential equation Mdx +Ndy =0 is exact i.e, ∂M∂y=∂N∂x ,then solution is        ∫y…

Q: 1. A certain ellipse is centered at the origin from which the major axis is always equal to 25 and…

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Q: Find the volume generated by revolving the area bounded by x² + 4x + 4y + 8 = 0 and y=-2 about the…

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Q: = Find the area bounded by the curves -x + y² = 8, x = -2y and y

A: Follow the procedure given below.

Q: For each of the following, state whether it has meaning. If not, explain why: (a) (ū. v) — |w| (b)…

A: We have to find the vector meaningfull

Q: 16. Let lim f(x) = -7, then what is lim (-9. f(x))? X-C A. - 16 C. 16 D. 63 B.-5

A: limit

Q: Find the Area of the Surface obtained by rotating the curve about the x - axis y = cosh x, 0 ≤ x ≤ 1

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Q: 4. Consider the plane : x + 3y - 2z = 6 and the line with parametric equations l: x=4-3t, y=2+t, z =…

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Q: 2. z = x + 2 У Х x

A: Solution

Q: y = (x² + 2)(x-3)

A: The objective is to find the derivative.

Q: d dx A.sinh(Inx) B.–sinh(Inx) sinh(Inx) C.- X -cosh(x) D. X cosh (Inx) =

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Q: For the following exercises, find aj dt and direct substitution. 226. f(x, y) = x¹, x=t, y=t using…

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Q: Consider vector v = (1,2,2), point A(2,5,4) and point B(-1,5,1) - In center-radius form, find an…

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Q: In x Compute -dx. 3√√/x 9 X 3 A²x²0 nx-x²²+ C A.- In 2/3 2 4 1 B.- - +C X 3 4/3 4 3 C.--(In x)x-4/3…

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Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (a) If Ř(0) = (-1,4,-5),…

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Q: Given the function f(x) = = Find the difference quotient Find f'(x) by determining lim f(x +h)-f(x)…

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Q: 2) Let f be continuous on [a, b], differentiable on (a, b) and positive (i.e., > 0) for all f'(c)…

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Q: I co cos³ x sin x dx

A: Given problem:- ∫cos3(x) sin(x) dx

Q: B. m(x) = D. h(x) = x+2 x²-4 28. What is the removable discontinuity of x²-4 the function f(x) : = ?…

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Q: Let line 1: x = = = and point P(1,0,1). 2 ● Find the set of parametric equations of the line…

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Q: √√f(x) x→ 3.h(x) 20. What is the value of lim A. C. - 12/2 6 B. -1 D. 21/2 5 I N|2 13 -?

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Q: 6. f(In x)² dx

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Q: smaller x-value larger x-value (x, y) = (x, y) = X X

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Q: Determine the value of x when the slope is its maximum for the function f(x) = 2cos (3x)

A: Given,  f(x)=2 cos(3x)

Q: The volume of a cube is increasing at the rate of 4cm³/min. How fast is the surface area increasing…

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Q: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the…

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Q: Consider the points K(-1,0, 7) and M(1, -2,5), the vector MN = (1,4, -3), and the line with symmetr…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: If fx √1- x4 dx = ge ½ A B 0 C D) 1 H|2 H|4 g(e) de, then 9

A: We can solve the given integral by using substitution.

Q: z = xey + y ex

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: chie in 4126 123V5LICE 3. A parcel of land has an area of 5 hectares. Express this area in square…

A: topic - unit conversion 1 hectare = 107639 square feel

Q: dx ex√4-e²x the integrand is transformed into? (a) cos² 0 (c) sin² 0 (b) sec²0 (d) csc²0 When the…

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Q: -0.45|-2.8x - 4.06| 2.5

A: Here we have -0.45-2.8x-4.06-2.5

Q: Advar Ex: If w = f(x,y,z), x=x(r,0), y =y(r, 0), z = z(r, 0), find wr, we? дw dz aw ax дw ду aw

A: We will use chain rule to solve this question.

Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² +…

A: We first graph x2+y2-6y=0 and y=6-x using a graphing calculator.  The shaded region will rotate…

Q: Using Pappus Theorem, find the volume formed by revolving about the x-axis the area bounded in the…

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Q: Compute : , log,(cosx) d dx - sin x A. (In 2). cos x 1 B. (In2).cosx -(In 2). sin x C. COS X -In2 D.…

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Q: Consider the vector-valued function R(t) = (t³ — t, 2t²,2 — 21.²). 1. Find ||'(t) || (Simplify your…

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Q: A product can be produced at a total cost of C(x) = 500 + 100x² + x³ dollars, where x is the number…

A: Solved below.

Q: Suppose g(x) = x²f(x) and it is known that f(3) = 5 and f'(3) = −2. Evaluate g'(3). gʻ(3) = =

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Q: ds Find the complete solution of = 8t³ √√s. dt

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Q: a. For the following function, find f'(a). b. Determine an equation of the line tangent to the graph…

A: This question can be solved using the concepts of application of derivatives.

Q: 1. Solve the differential equation (x-4y-3) dx-(x-6y-5) dy=0

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Q: Find the area enclosed by r = = √2 sin 0 and r2 = cos 20.

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Q: Given x = - ³²+2y — In(y + 1), find the arc length for 0 ≤ y ≤ 3 8

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