Find V · (F × G), if F(x, y, z) = 2xi+j+14yk and G(x, y, z) = xi + yj – zk. | V · (F x G) =

Q: Find V × (V × F) if F(x, y, z) = 6xyj+ 4xyz k. V x (V × F

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Find G'(x). In(9) G(x) = (4e- 7t + 1) dt G'(x) =

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

Q: Describe the graph of the equation. r = 4 cos t i – 14 sin t j + k O An ellipse in the plane z = 1,…

A: Here, the given parametric equation is: r=4 cos t i-14 sin t j+k⇒r(x(t),y(t),z(t))=(4cos t, -14 sin…

Q: Consider the matrix -8 A = 13 21 1 4 -2 15, Where a;, represents the entries for A, for i= 1,2,3 and…

A: Given,        -8    0    5 A= 13    21  1         4    -2   15 a ij represents the entries for A,…

Q: (-1)"2"x" n=1

A: We will use ratio test to find radius of convergence.

Q: an

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Q: 2x2 +4x - て +2

A: To evaluate the given integral.∫2x2+4x-3x2 dx

Q: +y = e=* sin x

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Q: Find div F and curl F if F(x, y, z) = 7y°z*i – 11xz'j – 6xy°k. 5.7 div F= curl F=

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Q: Find an arc length parametrization of r(t) = (e' sin t, e' cos t, le') r1(s) = (|

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

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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: 86. If f'(x) > 0 for all real numbers x and s(1) đt = 0, which of the following could be a table of…

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Q: |r(t) × r"(t)|| Use the formula k(t) to find k(t). 13 r(t) = ei + etj 30 е4 K(t) : e-t (25 el2t + 1)

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Q: Find the limit. NOTE: Enter the answer using round brackets. ) - () t2 + 8 1 lim tto \ 5t2 + 6'8t

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Q: 2 _9 ii)lim- t-3 t2+4

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

Q: n What is the closed-form expression for the series 2 (k-2)², k=1 37 A + 6 n³ -n²+ 13 B 6 6

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Q: 6. Find the indefinite integral. S 3x³ V3x4 + 7 dx (Use substitution method)

A: Solving the problem by finding the value of integration.

Q: ||r(t) × r"(t)|| Use the formula k(t) = to find k(t). 13 r(t) = ell'i+e"j -t. K(t) = %3D

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Q: Find the unit vector in the direction of (3, -2). Write your answer in component form. Do not…

A: We will find the unit vector.

Q: SHOW THAT THE DIFFERENTIAL EQUATION IS LINEAR EQUATION OF ORDER ONE 2. (y – 2)dx + (3x – y) dy =&

A: We can solve this problem as follows:

Q: Find the centroid of the region bounded by y = VI and y = x². U

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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: A forest fire is found at midnight. It covers 1100 acres then. It is spreading at a rate of f(t) =…

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Q: a) f(x) =(5x + 3)(7x² - 2) using the product rule b) f(x) = (3x? - 5) using the chain rule c) f(x) =…

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Q: 2. Compute Ja F · ds for F c(t) = (t , In(1+ t²), e*) for 0 <t < 1 VV, where V(r, y, z) = 4x² In(1+…

A: Find your answer below

Q: 6. Vectors i and v are positioned at 115° to each other such that lü| = 15 and l0| = 7. Determine…

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Q: y x = y - 2 y = 1 x = e -3 -1 1 2 4 | y = -1 3. 3.

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Q: 1. Do the integration by substitution for the following integral and find the value of definite…

A: We have to find the given integral value.

Q: Let be A, B, C three matrixes 30 1 B = z A = 2 y C = 5 13 -10, 10 What is the value for X that…

A: We will solve for x.

Q: Evaluate the indefinite integral: .3 dx x² – 2x + 5

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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

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

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Q: (6x- y+3)dx+(3y'-x-2)dy 6) Integration Factor Method rahee

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Q: Find the general solution of the differential equation. dy = xy + 3x dx

A: To find the general solution of the following differential equation.dydx=xy+3x

Q: Find the 4** x³ dx А. + c 4 In 4 В. + c 4 In 4 С. + c 3 In 3 D. 24 2 In 2

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Q: Solve the inequality involving absolute value. |x-3|/4<2

A: Given :        x-34&lt;2

Q: A ball is launched straight up in the air from a height of 5 feet. Its velocity (feet/second) t…

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Q: Question8: Choose one answer. You decide to collect a bunch of cans of soda and measure the volume…

A: To solve the following problem

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: (

A: We will find the centroid of the triangle.

Q: Use the One-to-One Property to solve the equation for x. 3x - 1 = 27 %3D X =

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Q: 1. Sketch a single graph of a function f(x) which satisfies all of the following the limits and…

A: The function satisfies,f-3=1, limx→-4f(x)=-1, limx→2-f(x)=-∞, limx→2+f(x)=∞, f'(4)=0f(2)=2,…

Q: Find curl (5z i + 6x j + 2y k). curl (5z i + 6x j+ 2y k) = ( i )i + ( i )j + ( i )k Save for Later

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 4yHx²j +42?yk. 5: 112. div F= curl F=

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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: Describe the graph of the equation. r = 7 cos t i – 17 sin t j +k O An ellipse in the plane z = 1,…

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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: 6 + (-3) + 0 + ..+ 411 = 97 (a* + 5) - 0 k = 1

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