Find the area between the curve y=2 and the chord joining the points (0,1) and (2,4). O 0.5608 O 0.6719 O 0.7820 0.8931

Q: Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 – x2 b.…

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Q: Q Find the deriva tive using the de fini tion (x)

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Q: Evaluate the improper integral |. 3.x dx or show that it diverges. +1 x?

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Q: x+1 dx

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Q: Find the values of c guaranteed by the Mean Value Theorem (MVT) for f(x) = =x + 7 over the interval…

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Q: e2x - e 2x 3. lim, 0 sinx

A: To evaluate the given limit.limx→0 e2x-e-2xsin x

Q: Use the linearization L(3,-2) (x, y) of f(x, y) = -x²y-xy² near the point (3, -2) to approximate the…

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Q: Evaluate the line integral / (9x + 10y)dx + (5x – 6y)dy along the curve C : a = 6 cos t, y = 12 sint…

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Q: Determine the value(s) of x where the tangent to g(x) = (x + 5)(x2 - 1) is parallel to y = -7x - 8

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

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Q: b) Use L'Hôpital's Rule to evaluate the limit L. e2x lim X→∞ x2

A: We can solve part in the following steps.

Q: Clear denominators in the following partial fraction decomposition and determine the constant B. 3x?…

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Q: 1009 1010 R= E (2k) =2+4 +6+ ... +2018 and S= 2 (2k- 1) = 1+3+5+...+ 2019. What is the value of R-…

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Q: 2r-4x2-x-3 dx x- 2r 3 In Ix+ 1 +3 ln|x-3| + C +1-3 ln|x-31+ C Option 1 Option 2 2 In |x + 1| - 3…

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Q: 3. Use the Fundamental Theorem of Calculus to evaluate the definite integral 16 x Vx dx 4

A: Given: ∫416xxdx Simplifing the given integral∫416xxdx=∫416x(x12)dx                 =∫416x1+12dx…

Q: Verify Green's Theorem by evaluating both integrals aN aM dy dA ду ax for the given path. C: square…

A: Application of integration

Q: Help Homer design a cylindrical silo to hold the output from his pet pig Harry Plopper. The silo…

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Q: Find V · (V × F), if F(x, y, z) = e2²i+ 7xe'j – 2e²k. - V·(V × F) =

A: Solved below

Q: Consider the following statements. 1-If B is a symmetric matrix of 9x9 so the elements b32 and bz3…

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Q: 7. a) Find the indefinite integral. (Remember to use absolute values where appropriate) 1 dx 4x -

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Q: 21 The function f(x) is represented in the following table. Give the best estimate for f(x)dx 3 9.…

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Q: d d Calculate r1(t) · r2(t)] and r1(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: Use the first six non-zero terms of the Maclaurin series expansions for sin x and cos x to…

A: From the Maclaurin series expansion of sin x and cos x: sin x≈x-x33!+x55!-x77!+x99!-x1111!cos…

Q: x-4 dx x2+2x-15 1 -In]x + 5 - Inlx - 31 +C 9 In|x +5|- In|x – 3| + C Option 1 Option 2 Ln x + 5)이 1…

A: Given problem:-

Q: Consider the function f(x): - 4x + 6x - 8. f(x) has a critical point at x A. Find the value of A: A…

A: For critical points ofa function we first find the derivative of the function and equate it to zero.

Q: L (21 +x+3)dx

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Q: Find div F and curl F if F(x, y, z) = 3e*"i – cos yj+ 7sin? z k. %3D div F= curl F=

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Q: 7. Determine the following general antiderivatives. cos (x) dx -dx sin(x) а. - b. 10 sin(x)cos(x) dx…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

Q: R be the region bounded by the curves y = 10 − x^2 and y = x^2 − 8x. Set up, but do not evaluate,…

A: Given query is to setup the integral for area .

Q: Find the volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y= 0, y = 7+a*…

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Q: d d Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: 1. A rectangular page is to contain 24 square inches of print. The margins at the top and bottom of…

A: The solution is given in the next steps.

Q: Evaluate the line integral, where C is the given space curve. xyeY dy, C: x = 3t, y = 2t, z 4t,…

A: Here we have to find line integral.

Q: 16. Find the volume of the region that lies under the graph of the paraboloid z = over the rectangle…

A: Here, to find the volume of the paraboloid z=x2+y2+2 over the rectangle R=(x,y)∈ℝ2|-1≤x≤2, 0≤y≤2

Q: Compute f(x)dx f(x) = { 2x if x <1 4 if x 21

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Q: Find the limits of integration ly, uy, Ix, ux, Iz, uz (some of which will involve variables a, y, z)…

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

Q: (a) Find the directional derivative of the function f(x, y) = 4.xy – x2 – y? in the direction of…

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Q: Find curl (3z i + 4x j + 6y k). curl (3z i + 4x j + 6y k) = ( i )i + ( i )j + ( i )k

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Q: Find the derivative of the vector function r(t) = ta x (b+tc), where (5,-4, 1), b = {(-4, –3,1), and…

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Q: Verify Green's Theorem by evaluating both integrals | y2 dx + x2 dy dA ду for the given path. C:…

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Q: Given the force field F, find the work required to move an object on the given orientated curve. F =…

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Q: i(x) = 2-0.8(x-43.79)

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

Q: Let be A, B, C,x. 5x5 matrixes such that A, B and C can be inverted such that AXB" – 151, = c-1…

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Q: Evaluate and simplify: 4sin(4)- csc(-) 2 A 1-2/7 B 1+2/7 -1-2/7 D -1+2/7

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Q: an

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 3 y…

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Q: 2X メ→チ 7-x

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Q: Mic differentiation to Find der :Vative Of Y «in(x+7) x+7)* (In(x+7) + X. X-1 H7)* (x+7) t x+7

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) sin(9t), lim t-0 e5i +…

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Q: P1. 18. Which of the following is true? Select one: O a. AxB is the same as BxA O b. If vector A is…

A: Vector