Find the volume of the solid under the surface z = × siny that lies above the rectangle R = [0,1] x [0, pi].

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A: Let the given function f(x)=x3cos4x

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A: We can answer both the question as below

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Q: Solve for x. log₂ (x-6) + log₂ (x-4)= 3

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Q: 10. lim, -6(x-sin'x)(cs scx)' X)( csC X

A: A detailed solution is given below.

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Q: Solve the following equations:* (DS+D¹-7D³-11D²8D-12)y=0

A: The given differential equation,D5+D4-7D3-11D2-8D-12y=0

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A: Given query is to find derivative if the expression.

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Q: For the function f(x.y.z) = sin'(5xyz), find fy. fy. and f (Type an exact answer, using radicals as…

A: f(x,y,z) = sin-(5xyz) fx = derivative with respect to x fx = 5yz/1-25x2y2z2 fy = 5xz/1-25x2y2z2 fz =…

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A: Topic:- function

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Q: 4. It is estimated that x months from now, the population of a certain town will be changing at a…

A: First we will integrate p'(x) to find the function p(x) and then we will find the population 27 from…

Q: of and дх of Find for the following function. dy f(x.y) = (x' - 4) (8y + 7) of dx

A: To find ∂f∂x and ∂f∂y for the following function.fx, y=x5-48y+7

Q: Solve the following equations: (D3³+ 3D²+ 3D + 2)y = 0

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Q: What is the allowable error in measuring the edge of the cube that is intended to hold 8 cu.m. if…

A: Given problem:- What is the allowable error in measuring the edge of the cube that is intended. to…

Q: 6 4 Verify that for f(x, y) = 3x°y* - 4x°y°. дх ду ду дх of

A: Given problem:-

Q: 1. Given f(x) =.9x) = 2x – 7, and h(x) = , find the following. a) The domain of f(x). Write the…

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Q: Find a value c that verifies the conclusion of the Mean Value Theorem for the function f(x) = x² on…

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Q: 2. Consider the following vector function: r(t) = = a cos wti + a sin wtj + bwtk, where a, b and w…

A: We need to find radius of curvature.

Q: dy Find if dx\x=0 (x – 2)³ - (2x + 1)* 2. +৪ Use logarithmic differentiation.

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Q: Find dyldx at x = pi/3* y = sinh'(2x) O 0.8617 O 0.6817 O 0.6871 O 0.8671

A: This question is based on chain rule differentiation.

Q: of Find - for the following function. and 5xy f(x.y) = e In (3y)

A: Given: Now,        ∂ ∂ xe5xyln3yTreat y as a constant=ln3y∂ ∂ xe5xy=e5xy∂ ∂ x5xy=ln3ye5xy· 5y

Q: Given cost and price (demand) functions C(q) = 130q+47,500 and p(q) = -2.8q +820, how many items…

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Q: Find f, fy. f- f(x.y.z) = 3x - 4y 2. 2 +z?

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Q: Let f(t) = 3t4 - 6t+ 3et. Then f'(t) =

A: To find f'(t)

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

Q: Velocity 3.5 3 2.5 2 1.5 1 0.5 1 2 3 5 6 Time (s) Velocity (m/s) 4.

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Q: Find the exact value. (a) sin( (b) arctan (-) (c) arccos (cos())

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Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

A: Given query is to find integral converges or diverges.

Q: cos\theta =(1)/(3)and \theta  is in quadrant IV, then cos(\theta )/(2)

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Q: -1. For the function f(x,y,z) = sin '(xyz), find fx, fy, and f₂. fx (Type an exact answer, using…

A: Given query is to find indicated derivative.