Given the figure and f(x) f(x)d(x) = 1.05, estimate: (a) f(x)dr (b) f(x)dx (c) The total shaded area

Q: _3. S(3v +) dx = D(x + 3) + C

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Q: O 10(x2 +y²).dx+3.x.y.dy

A: As we know from the Green's theorem: ∫CMdx+Ndy=∫∫R∂N∂x-∂M∂ydA   Given ∫C10x2+y2dx+3xydy…

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

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Q: A note card company has found that the marginal cost per card of producing x note cards is given by…

A: Given : Marginal cost in cents is C'(x)=-0.08x+75    , for x≤1000   To Find : Total cost for…

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Q: Q-3: [5 marks] Use the definition of the derivative to find the derivative of the function f(x)= /1…

A: Given

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: 1.SUpPose that fCx) = 3x(x-1). Find the critical numbers of fiX). Use them to detemine on which in…

A: We need to find critical point and interval of increase and decrease.

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Q: Test the series below for convergence using the Ratio Test. 57 n! n=1 The limit of the ratio test…

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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: Evaluate the indefinite integral as a power series. x² In(1 + x) dx f(x) = C + E What is the radius…

A: To evaluate as a power series: ∫x2ln1+xdx We can write ln1+x as ∫11+xdx ⇒ln1+x = ∫11--xdx Writing…

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

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Q: Use l'Hôpital's Rule to find the limit. x11X lim x→0 11* – 1

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Q: 10 -5 -10 %3D -2 -4

A: The answer is in below steps.

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A: Explanation of the answer is as follows

Q: Find Y for this equation: dx y3 5x?y – 6x [no need to find y in terms of x]

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

Q: 2) The rate of change of an electrical current, i, in a microprocessor circuit is given by di 0.4t –…

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Q: 3. A 1 000-metre track is to be built with two straight lines and semicircles at the ends as below.…

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Q: 1. Find the area between y=x and y=x' fromx=-1 to x-1. 2. Find the area of the "triangle" region…

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Q: 19 |x* sin xdx

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Q: COLUMN A COLUMN B 1. S(E-0) dx =- 4 In|x| + C A. 4x 3D B. 4* S) dx = 6V7 + c S(3vx + dx = D(x + 3) +…

A: Solution

Q: Find the quotient and remainder on dividing:  8x^3 + 12x^2 + 1 by 2x + 3

A: Given query is to the quotient and remainder.

Q: na "rx) ax = 7, evaluate Given dx - 0 dx. dx dx. (c) dx. (d) 3(x) dx.

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Q: Find the area under the given curve over the indicated interval. Q 14- y= 2x [1, 6] ... The area…

A: Given: y=2x, (1,6)

Q: Find the gradient vector field (F(x, y, z)) of f(z, y, z) = e®2z + $y + 2= F(1, y, z) =

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Q: Find any critical numbers for f and then use the second derivative test to decide whether the…

A: For finding critical point f'(x) = 0

Q: у" — бу' — 7у%3D11 sin 4x -

A: We have to mention the general form of the particular solution

Q: 9-у 5. S dy dx 6. S e 2х+1

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Q: x²+2x-63 1. a) Find the value of lim, x-7 10*-10-* b) Evaluate lim,¬ 10*+10-x

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Q: dx e 2x+1

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Q: 4. Fill in the blank with "all", "no", or "some" to make the following statements true. Note that…

A: Explanation of the answer is as follows

Q: 1. S 5e*dx 2. S(2 – 3e*) dx

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

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Q: Evaluate the double integral / (a (x² ,2 + 8y) dA, where D is bounded by y = x, y = x°, and x > 0.

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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: Find the point of diminishing returns (x,y) for the given function, where R(x) represents revenue…

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Q: 1. Given the function f(x) = Vx5 – 3Vx², find the interval(s) of increase.

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Q: Find the equation of the line with slope −2 which goes through the point (9,−7).

A: Find the equation of the line with slope −2 which goes through the point (9,−7).

Q: Complete parts (a) through (c) for the following function. f(x) = - 3x + 3x - x-1 (a) Find intervals…

A: Here we have to use the concept of derivatives.

Q: j. For any 3 x 3 linear system AX = 0 if det A 0 Then Select one: O the linear system is…

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Q: Find the open intervals where the function is concave upward or concave downward. Find any…

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Q: %3D Find the most general antiderivative or indefinite integral. (Hint: 1+ tan 0= sec0) (-3-3t - 3…

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Q: 27t3 dt

A: Given query is to find the integral.

Q: Fill in the table and then sketch the vector field. z| y F(z, y) = (, %3D 20 0 2 -2 -2 2 -2 -2| -2 2…

A: Here, to fill the table and then plot the vector filed.

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

A: Given data÷

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

A: