27х3-8а3 y3= y= 3x-2a Зх-2а

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

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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: Consider the function f(x) = 1/3x3 + 3/2x2 - 4x. At which point(s) is the slope of the tangent line…

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Q: 3. 1- xZ dx

A: The integration of the integral is x4sqrt(1-x2), limit from 0 to 1.

Q: r(4) (arcsin(t), arcos(1),0

A: Given: rt=arcsint, arccost, 0   As we know that; ddxarcsinx=11-x2ddxarccosx=-11-x2

Q: (b) Ir(t) x u(t)] dt (i) Find the product first, then differentiate. (ii) Apply the properties of…

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Q: (1 point) Use the Divergence Theorem to calculate the flux of the vector fields F, = -Szi + 5xk and…

A: Find your answer below

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by…

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Q: (x + 1) f' (x) = f(1) = 5 x,

A: Solution is given below:

Q: ,2 COS cos n Σ n3 n=1

A: Given problem:-

Q: Find the S(x* +) dx xe-1 А. 1x? + c e-1 4e xe+1 В. Ix2 + c e+1 2e xe+1 С. 1x3 + c e-1 Зе xe+1 1 D.…

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

Q: Find V x (V × F) if F(x, y, z) = 4xyj+ 9xyz k. V x (V × F)

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Q: Given the following functions: f(x) = cos(x) g(x) = x + 1 Find f(g(x)) and 8(S(x). (Use symbolic…

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Q: 4 y=V4x- 2/2x

A: Topic = Derivative

Q: Find the derivative of this function

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Q: 3x?+4x-7 ii) lim x2+9 X00

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

Q: 2. Find the area of the parallelogram whose vertices are given by: P: (1,2, –1), P2 = (4, 2, -3), P3…

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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: n/2 c sine Evaluate the iterated integrals J. r cos e dr de 0. A 1/6 B 1/2 c) 6 D) 11/9

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Q: cos (0 + 11) y = Use symbolic notation and fractions where needed.) dy -4 cos (0+11) sin(0+11)| do

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Q: stimate using the trapezoid rule and Simpson's rule for et dx;n3D8 -2x+5

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Q: Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the…

A: We need to set up and evaluate integral.

Q: Find the Taylor series centered at a = 0 for the following function: -7x f(x) = e 8. Answer: n=0 (Be…

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Q: Let I be the flux of G = (2e", 4x°e*“, 0) through the upper hemisphere S of the unit sphere. (a)…

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Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.…

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Q: Sketch the region enclosed by the curves and find its area. у %3 сos 9x, y —D 0, х - x = 18' 9 NOTE:…

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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 curl (9z i + 10x j+ 7y k). curl (9z i+ 10x j + 7y k) = ( i Di + ( i Oj + ( i )k

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Q: 34 Count lim (1+x) F b) lim (1-x)* メ→0 The limit in (a) determines e. What special number does the…

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Q: Evaluate the limit using L'Hospital's rule: Lim0+1 In(x+1) 2xe"

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Q: 1. dt 15. y= 17. y 0 tan 0 d0

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Q: Find an equation of the hyperbola having foci at (3, -11) and (3, 7) and vertices at (3, -4) and (3,…

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Q: Find the area bounded by the graphs of 1, y= and X=1 (Ao the right)

A: Find your answer below

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

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Q: find area OPShaded Pegion ニ 16x

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 3 cos(t)i + 5 sin(t)j…

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Q: Зху dx + 4xy dy %3D i 63

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Q: Determine the equation of the tangent to the graph of the equation xy – 2x'y-3ry + 5y – 4 = 0 at the…

A: To find the equation of tangent to the given equation at (1,2).

Q: 1. Find the particular solution of the differential equation that satisfies the initial conditions.…

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Q: Evaluate the definite integral. 9ti + 3t°j + Vtk) dt

A: The given definite integral,    ∫-119t i+3t3j+t3kdt

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: (c) f''(x) = cos x, f(0) = 1, f'(0) = 2, f"(0) = 3.

A: Explained below

Q: Find V. (V × F), if F(x, y, z) = 5e"*i+ 6xe®j– 2ek. V · (V × F)

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Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

A: Given points,  P(0,0,0), Q(4,2,4)

Q: Find V × (V × F) if F(x, y, z) = 4xyj+2xyz k. V × (V × F) :

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Q: Describe the graph of the equation. r = (5 – 31) i – 81 j O It is a line in 2-space that goes…

A: Given : r=(5-3t)i-8tj

Q: sin° xcos xdx x cos'

A: We will use substitution method to solve this definite integral.

Q: af Find for the function: f(x, y) = xcos(xy) + 2xy2

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Q: Using the substitution u = sin (x), or otherwise, find the exact value of %3D J sin° (x) cos (x) dx.…

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Q: The strength E of an electric field at a point (x, y, z) due to an infinitely long charged wire…

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