Find the unit tangent vector to the curve at the specified value of the paramet r(t) = 4 cos(t)i + 4 sin(t)j, t = 3 3

Q: Use the function to find the image of v and the preimage of w. T(V1, V2) = (V1 + V2, V1 - V2), v =…

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Q: $3000 is invested in an account at interest rate r = 0.035, compounded continuously. (Round your…

A: Given that $3000 is invested an account at interest rate r=0.035, compound continuously. we have to…

Q: Verity Gauss' theorem for the vector feld f (x,y, z)= (y,x,2) on the surface of the sechere with…

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Q: 10 10 f (x) dr=17 and | f (x) dr=12, then f (x) dr=5. A) True B) False

A: Given query is to find statement true or false.

Q: 2) Evaluate the integral S inx dr 2.

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Q: Use double integration to find the area of the plane region enclosed by the given curves. y = 25 sin…

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Q: Find the general solution 2x'y - (2x + y) = 0

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Q: 2. If ā = 3i - 27 + ok and b =(4,-1,-6) compute ā xb. 3. Find a vector that is orthogonal to the…

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Q: Use partial fractions to evaluate the definite integral. Use a graphing utility to verify your…

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Q: Evaluate the integral 29 (2° – 2) dx -y making the substitution u = x° – 2. + C NOTE: Your answer…

A: Given query is to find the integral.

Q: Question 5 Find the volume of the solid that results when the region enclosed by the given curves is…

A: To find the volume of the solid that results when the region enclosed by the given curves is…

Q: Express the integral as an equivalent integral in which the z-integration is performed first, the…

A: Here,  0≤x≤4-yy≤z≤8-y0≤y≤4 To change the order of integration to dx dz dy to dz dy dx

Q: 1) What are the equations (4 of them) that show the relationship between polar and rectangular…

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Q: (2sinx-sin2x' 1. lim x-sinx

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Q: Suppose that f (x) is a function such that lim f(x) and lim f (r) both exist. r3+ Does this mean lim…

A: Use limit definition to prove the limit.

Q: Find the general solution of the equation. Express the solution explicitly as a function of the…

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Q: Evaluate the double integral.

A: Given

Q: Find the sum, if it converges. Σ6 i= 1 The sum is (Type an integer or a simplified fraction.)

A: In this question we have to find the sum if the series is converges.

Q: Solve the following differential equations of dy 1 -·y = xy'; dx

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Q: For problems 3- 4 determine the angle between the two vectors. 3. p 9i-j, =-37-6j

A: Topic = Vectors As per guidelines , At a time only one question can be answered. please repost for…

Q: Question 30 Find the curvature k and radius of curvature R for the curve at the given point. y = cos…

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Q: For problems 1- 2determine the dot product, a-b. 1. ā = 9ĩ -8k , 5 = (3.-2.1) 2. and the angle…

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Q: Use double integration to find the area of the plane region enclosed by the given curves. y = 81 – x…

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Q: Find the area of the region enclosed by the curves y=x2−2 and y=2.

A: Integration is done after calculating the intersection points of both the equations.

Q: dy = 2 – y dx Find the correct direction field for the differential equation ノー\\ ババーと

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Q: ​(A) Find the average value of the function over the indicated interval.   ​(B) Graph the function…

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Q: Find the area of the region enclosed by the curves y=x2−1 and y=8.

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Q: Evaluate the sum using the given information. X1 = - 3, X2 = - 1, and x3 = 2 Xj - 5 Σ 2x; + 4 3 j= 1…

A: Solution is given below:

Q: Let f(x) be the function 2a² – 4x + 11, Then the quotient f(2 + h) – f(2) - can be simplified to ah…

A: The equation of line between two points;(4, -3) and (-3, 0)f'(4)=0+3-3-4=-37passes through (-3,…

Q: Evaluate the cylindrical coordinate integral. π θ/π 74-2 zdzrdrde 0 0 - /4-12 a 0/n 7/4-12 zdzrdrde…

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Q: A farmer finds that if she plants 40 trees per acre, each tree will yield 20 bushels of fruit. She…

A: Harvest

Q: If {(=)dz = f(x)dx f(x)dx + f(x)da f(x)dx, what are the bounds of integration for the first…

A: Solution:

Q: b) X, + X2 - 2 X3 +Xy = a) 5X +2y = 1 3X +2y %3D = 1 Xz - X3 +2 Xy = 1 %3D = 5 X - 5y = 6 c) 2x, +8…

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Q: Solve the following differential equations of e • dx+2(xe" – y)dy = 0;

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Q: Solve the initial value problem. 4 y(x) = 4 sec(3.xr) tan(3x) ; y(7) = 3

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Q: Find the foci of the hyperbola. 2-9y-90y-234 = 0

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Q: 4- if U(x,y) = x2 + 2y and x(r, t) = r sint, y(r,t) = sin?t, au find 1- ar au and 2- at au 1- ar ди…

A: Given that,   U(x,y) = x2+2y   and x(r,t) = rsint,     y(r,t) =sin2t we have to find ∂u∂r,    ∂u∂t…

Q: Solve the problem. 12-64 For what values of t is r(t) = ti+ j continuous? 12 + St O {te D: t#0 and…

A: We have to find out

Q: d f'(3).

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Q: Find the derivative of the function f(x) = 9r( – 5x + 6z). %3D f'(x) =

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Q: sin e = If and 0 in the first quadrant, find Cos 20

A: A detailed solution is given below.

Q: www 1D syppose that a sequence CanZ is definel by the envations az =2 cand anti = following is true…

A: Clearly,

Q: Write an iterated integral for d. dA over the region R described to the right using R a. vertical…

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Q: e8/n Σ 7 = 1

A: Given query is to find series converges or diverges.

Q: 7 Evaluate the sum i(3i + 2) i=1

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Q: Evaluate the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

A: We have to find integral

Q: Express the integral as an equivalent integral in which the z-integration is performed first, the…

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Q: 9. 5+ 8 7- 6- 3 5 4 2 g(x) 2 h(x) 1 1 1 2 3 x-values 4 5 1 2 3 x-values 4 If f(x) = g(h(x)), then…

A: Explanation of the answer is as follows

Q: Solve the differential equation for general solution 7y6dy = 8x

A: Given query is to find the solution of the differential equation.

Q: Question 5 Find parametric equations for the line described below. The line through the points P(-1,…

A: Given: P-1,-1,-1   and 6i-3j+3k