Q6A)If y = cos ¹) prove Zyy + z = 0.

Q: A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles…

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Q: Find the area between the curve and the x-axis over the indicated interval. y = 6 x 10 [1, 10] The…

A: See this solution in below

Q: Use the properties of the derivative to find the following. r(t) = ti + 4tj + t2k,   u(t) = 5ti +…

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Q: Evaluate the integral. Select the correct answer. 6 6 x In (19x) - 12/15 x + C none of these 16 x In…

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Q: Solve

A: Topic:- solution of differential equations

Q: - 1. 1 [(ow + √w) dw

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Q: Consider the following information fz(x, y) = 2xy - 2r³ and f₁(x, y) = x² + y² – 6. Use the Second…

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Q: 15. Show that the equation, ³ + e* = 0 has exactly one real root.

A: we have x3+ex =0to check number of roots we can draw graph of both and check number of intersection

Q: 3. f(2x + 3)² dx

A: I have stated the used formulas in the solution

Q: 14. Given the function f(x) = 3x³ – 48x find the following: (Round to 1 decimal place) a) The x and…

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Q: - [² Suppose F(x)= = sin(t) dt. Use the Fundamental of Theorem of Calculus to calculate - (F(x³)).…

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Q: 1 a. Determine whether the Mean Value Theorem applies to the function f(x) = x + on the interval…

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Q: 2x et. Vi-eza ex fer.

A: ∫ ex1-e2xdx=∫1-u2du=∫1+cos2v2dv=12·∫ 1+cos2vdv=12∫…

Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R…

A: Here we have to find the volume.

Q: Use the derivative f'(x) = x²(x - 5)(x + 5) to determine the local maxima and minima of f and the…

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Q: 1) Simplify the expression for f(x + 1) - f(x) where f(x) = e2x - 1) . ) 0 (2 - 1) b) O (2-1)(2 - 1)…

A: option (b) is correct. see below the calculation

Q: The one-to-one function fis defined below. 3 f(x)=√√/2-x+7 ¹(x), where f¹ is the inverse of f. 1…

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Q: Use Figure 1 to evaluate the trigonometric function. Enter the exact answer. tan A = B 10 Figure 1 A…

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Q: Use identities to find values of the sine and cosine functions of the function for the angle…

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Q: Find and classify the critical points of f(x,y) = 4r+20² - y²

A: Find and classify the critical points of f(x,y)= 4x+2x2-xy2.

Q: Find the following for the given equation. r(t) = (t² + 3t)i + (t² - 3t)j (a) r(t) = (No Response)…

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Q: Set e кад dx

A: To solve the following problem

Q: Problem3 Find a curve in the xy-plane passing through the point (1, 2) and for which th normal line…

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Q: Use the difference anti-an to show that the given sequence {a} is strictly increasing or strictly…

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Q: Evaluate the integral. Select the correct answer. 1 15 cos ²6 x - = cos 6x + C cos³6 6x- 18 O…

A: Given :∫sin36xdx

Q: Find a bif a= (4, - 1,5) ar . b = (-3, 8, 5).

A: Here we will find whether given vectors are orthogonal or not,

Q: Approximate the area under the curve graphed below from x = 2 to x 6 using a Left Endpoint…

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Q: 150 Find the consumers' surplus for a product if the demand function is given by D(x) = 3+x Answer…

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Q: Find the function F that satisfies the following differential equation and initial conditions.…

A: This question is based on diffrentiation equation and solved using Laplace transform.

Q: Q3 Let A(1,0,-1), B(-1,2, 1), and C(1,2,-2) are the three points in a 3D coordinates system. a)…

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Q: The graph of f is shown in the figure to the right. Let A(x) = for f. Evaluate the following area…

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Q: A - 3 In 1x³ 3x²1+C BIn 1x³ 3x²1+ C x²–2x x3 3x² C dx In 1x³ 3x²1+C In 1x³ 3x²1+ C -

A: The given integral,    ∫x2-2xx3-3x2dx

Q: Problem3 Find a curve in the xy-plane passing through the point (1, 2) and for which the normal line…

A: Here we have to find the equation of curve.

Q: Find all solutions of the equation in the interval [0, 21). 2 cos²x=2+ sinx Write your answer in…

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Q: Solve the given differential equation by undetermined coefficients. y" + 5y = -180x²e5x y(x) =

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Q: A particle in R2 has a velocity function of v(t) = (3t²-4, 6t + 2) (given in m/s). After moving for…

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Q: Evaluate the ff (show all steps) dx (4-x²) 3/2 √

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Q: 2. Approximate √64.1 by using linearization and use a calculator to compute the percentage error.

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Q: The area enclosed by the curve y² = x(1-x) is given by .

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Q: Sketch the function  f(x)=-x3-3x2

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Q: lim X→+ 2 In x² 3 In (x+4) ³

A: This question is based on limits solved using L hospitals rule.

Q: Find the annual percentage yield (APY) in the following situation. A bank offers an APR of 5.4%…

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Q: Calculate the following antiderivatives: (a) ∫ 8t− 6t^6 −5dt =  +C. (b) ∫ 1/u^7/4 + 3.5 sqrt u du…

A: a) Given:       ∫8t-6t6-5dt  =∫8t dt-∫6t6 dt-∫5 dt taking constant out     =8∫t dt-6∫t6dt-5∫ dt…

Q: Define a polynomial function with all of the following properties. Roots: x=7, x=-8, x=0. It bounces…

A: Given problem:- Define a polynomial function with all of the following properties. Roots: x=7, x=-8,…

Q: Evaluate the ff (show all steps) S COS (Inx) dx

A: See the details solution in below

Q: 6. The acceleration of the position function s(t) = 4t² - 8t + 2 when t = 7. a) 7 b) 48 c) 142 d) 8

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Q: S tanx secx dx

A: We have to evaluate the given integration.

Q: The force exerted by an electric charge at the origin on a charged particle at the point (x, y, z)…

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Q: 4. At which points does the function f have absolute maximum or minimum, or local maximum or…

A: Absolute minimum:- Minimum value of total function Absolute maximum:- Maximum value of total…

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

A: We have to find r(t).