67 |xsin 3xsin 2xdx

Q: 1. Find the area between y=x and y=x' from r%3-1 to x%-D1.

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

Q: 3. A body is moving in simple harmonic motion with position s(t) = 3 + 2sin4nt. At what time in the…

A: s(t)=3 + 2 sin4πts'(t)=0+2 cos4πt (4π)s'(t)=8π cos4πts'(t)=08π cos4πt=0cos4πt =04πt =π2, 3π2,…

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = tan(6r + 2y + 2) . F(2, y, 2) =

A: Find the gradient vector field

Q: (a) Find an equation of the tangent plane to the surface at the given point. x² + y? + z? = 14, (1,…

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Q: A rectangular plot of land is to be fenced in using two kinds of fencing. Two opposite sides will…

A: A rectangular plot of land is to be fenced in using two kinds of fencing.Two opposite sides will use…

Q: 80. An electronics company is deciding whether or not to begin producing MP3 players. The company…

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Q: . What is the outer function? 2. Find dy/du. 3. What is the inner function? 4. Find the derivative…

A: see below the answer and calculation

Q: Given the function f(x) = Vx5 – 3Vx2, find the interval(s) of increase.

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Q: the solid

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Q: dx 4. J 1+ Vx -2

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Q: 5. Figure below shows triangle AOC inscribed in the region cut from the parabola y=x by the line…

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Q: 3. Find the area bounded on the right by x+y=2, and on the left by y=x and below by x-axis.

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Q: (a) Find an equation of the tangent plane to the surface at the given point. x2 + y? + z? = 14, (1,…

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Q: 6. Find the area bounded by:

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Q: 6.26. у - Зxу%3D0

A: Topic = Differential equation

Q: Jcos xdx Scos" xdx 10 12 fcos? xdx

A: 8.)∫-ππcos2x dx ( since, f(x) =cos2x , If f(x) is an even function i.e:  f(-a) = f(a)then ∫-aaf(x)…

Q: 12 Estimate the integral x°dx using a left-hand sum and right-hand sum with n = 4 subdivisions.…

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Q: 5. Compute the arc length exactly y =x² -In x , 1 sx< 2

A: Given : y=14x2-12lnx , 1≤x≤2   To Find: Arc length

Q: Evaluate this integral where C is a positively oriented closed curve delimiting the area D which…

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Q: Solve the given item below. Write your answer on a separate sheet of paper. A vertical liquid…

A: Volume of cone(V)=13πr2hr8=h22⇒r=4h11Substitute in the volume formulaV=13π×(4h11)2×h   V =16363πh3

Q: Determine the parametric equations of the path of a particle that travels the circle: (x-4)2 +…

A: We have to find the parametric equations.

Q: | vũ du b. y = sin x с. y = 3t? dt ctan x

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Q: 51 |x* sin 3xdx 2 53 [x' sin 3xdx 55 sin 3xsin 2.xdx

A: As per the guidelines I am supposed to do the first question among multiple questions. So I am doing…

Q: is displaced 8 cm from its equilibrium 4.A pendulum has a length of 40 cm. position and then…

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Q: Sketch the region whose area is given by the definite integral. хр y3 Use a geometric formula to…

A: Given query is to find the value of the integral

Q: 3. The position of a Roomba is given by the function s(r) = r –21² + 120r, where time, 1, is in…

A: In order to solve this question we need to get the velocity and acceleration function.

Q: 11 6 69 16 -14

A: This question based on finding inverse of matrix and matrix multiplication.

Q: Find the exact value of arc length of the semicubical parabola y2 = x³ between the points (1,1) and…

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Q: Find the area bounded by the graphs of the indicated equations. 12- 10- 8- 61 4-f(X) 2- X= - 3 X = 3…

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Q: Jxcos xdx

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Q: 1. For y=In2x, determine the equation of a tangent line parallel to 2x-3y+1=0.

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: In(1tcos 3x) 10. dx 1+cos 3x + C S (cos x)(sin?x)dx = 2 s In(3x) dx 11. + C 5in (1x) + C 12. %3D

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Q: (-1)²-1n n+vn b) an (Hint: Show what happens when n is odd and when n is even) %D

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Q: raphs and Derivatives he given graph is the graph of f': the derivative of some function…

A: We need to find interval and draw graph.

Q: Use cylindrical coordinates. Evaluate (x + y + z) dV, where E is the solid in the first octant that…

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Q: Find the solution. y'- ty = ty" y-2-

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Q: Consider the points A(1,-1, 4), B(2, –3, 2), C'(-1, –2, 2), and D(4, 3, -6). (a) Find the volume of…

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Q: How many terms of the Maclaurin series of f(x) = ln (1+x) are needed to compute In(1.5) to within an…

A: Given f(x)=ln(1+x) We want to calculate number of terms of maclaurian series required to calculate…

Q: Suppose that the graph below is the graph of f'(x), the derivative of f(x). Find the open intervals…

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Q: 9-у 5. S dy dx 6. S e 2х+1

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Q: Test differentiability at x = 0 and x 1 for the function x3 + 2x; х — 2; 1 0 <x<1 f(x) = x 2 1 x +…

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Q: 8 Jcos xdx Scos xdx 10 12 Scos? xdx

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Q: Find an equation of the tangent line to the function y 3x2 at the point P(1, 3). = Soluti

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Q: Consider the function, whose graph y = f(x) is shown below. -3 -2 What is the set of values of x E…

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Q: S 2+3* dx = 4 F. 2Vx 5. In 8 G. 8* S(D-) dx =: Inlxl 6. 2 In 3 H. 2x

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Q: A culture of the bacterium Salmonella enteritidis initially contains 50 cells. When introduced into…

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Q: The graph of f consists of line segments, as shown in the figure. Evaluate each definite Integral by…

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Q: 4. (i) Use the parametric equations of an ellipse, x = a cos (t) , y = b sin (t), 0 < t 2m, to find…

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Q: Under certain​ conditions, the number of bacteria present in a colony is approximated by…

A: Given, f(t) is the number of bacteria present at time t in minutes. f(t)=(A0)e0.022t A0= 2100000…

Q: 1. Find the second derivative for f(x) = (2r² – 3)* (Answer should be in simplified factored form…

A: Given problem:- Find the second derivative for f(x) = (2x2  - 3)8