Find the domain of r(t) and the value of r(to). | NOTE: Round your answer to two decimal places when needed. r(t) = cos(rt)i – In(t)j+ vt – 14k; to = 15

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) : = 6ti –…

A: Solution is done in step 2

Q: Let y = (3x + 2 sin(x))*. Find f(x) and g(x) so that y = f(g(x)) and compute the derivative using…

A: Here the given function is: y=(3x+2sin(x))4

Q: 4 y=V4x- 2/2x

A: Topic = Derivative

Q: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere X y² +…

A: We have to find the volume of the solid.

Q: Evaluate the line integral (4х + 5у)dx + (За — 6у)dy along the - curve C : x = 10 cos t, y = 20 sin…

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Q: In sketching the graph of y=f(x) = 2sin -5, we translate the graph of y=2sin by 5 units downward and…

A: To translate the given function.

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize…

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Q: In this question, the power series method is to be applied to find the general solution of a…

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Q: Use a triple integral to find the volume of the solid in the firsy octant bounded by the coordinate…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = Y, (1, 5, 5) %3D…

A: Given problem:- Find an equation of the tangent plane to the surface at the given point.   f(x, y) =…

Q: Evaluate the iterated integral. 4ze dy dx dz

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Q: Evaluate the iterated integral. /8 3/y sin y dz dx dy Jo

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Q: Describe the graph of the equation: r = 5ti – 8j + (1 + 5t)k. [Choose the correct answer.] O The…

A: Given, r= 5ti -8j +(1+5t)k Therefore, The equation is given by, r= <0,-8,1>+t<5,0,5>

Q: Find the area of the surface that is generated by revolving the portion of the curve y= X between x=…

A: We can solve as follows

Q: Find the centroid of the region. NOTE: Enter the exact answers. (7, g) = |(?, ?) y = 1

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Q: The graph of y=- 50co has a horizontal shift of A units with respect to the graph of y= - 50cos(x).

A: This question is related to Trigonometric functions, we will solve it using given information.

Q: Find the area of the region inside the circle r = 12 sin 0 and outside the cardioid r = 4+4 sin 0.…

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Q: 1. Find the equation of the tangent line to the curve x = e', y = et att = 1. 2. Find all values of…

A: tangent property

Q: ... 3x+ 2y + 4z = 12 12 15

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Q: Sketch the region enclosed by the curves and find its area. y = cos8x, y = 0, x = π/16, x = π/8

A: Given: y = cos8x, y = 0, x = π/16, x = π/8

Q: Evaluate the definite integral. 9ti +3t'j + Vtk) dt

A: The given integral,          ∫-119t i+3t3 j+t3kdt

Q: 5 S Ix² x- 6|dx -5

A: The given integral,            ∫-55x2-x-6dx

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: Find the approximate area under the curve of f (x) = x< +1 from x = 0 to x = 2, using 4…

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Q: Evaluate the definite integral. (9ti + 3+j + Vik) dt 9ti + 3tj tk dt

A: Topic = Integration

Q: Find [r(t) · u(t)] and [r(t) x u(t)] in two different ways. dt dt r(t) = cos ti + sin tj + tk, u(t)…

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Q: Evaluate the integral by choosing a convenient order of integration: x cos(xy) cos' (Tx) dA; R 0, x…

A: Given

Q: Evaluate the iterated integral. x dz dy dx 128/15 16/89 23/6 6.

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Q: Express the iterated integral as an equivalent integral with the order of integration reversed. 30…

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Q: sider the scalar function: f(x, y) = sin(3x)ey I the gradient: Vf(x, y) I the Laplacian: v2 f(x,y)…

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Q: Determine the volume of the solid obtained by rotating the region bounded by y=x^2-4x+5, x=4, and…

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Q: The integrand of the definite integral is a difference of two functions. Sketch the graph of each…

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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: Find the area of the region(s) enclosed by the curve f(x) = x°, the x-axis, and the lines x =-1 and…

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Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). 13 r(t) = t'i+ t3j K(t) =

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Q: dy Compute the derivative y dx y = 5x4 – x-4 (Express numbers in exact form. Use symbolic notation…

A: Given,y=5x4-x-4  Formula: If, y=xn then, y'=nxn-1

Q: Question 15 1-sine Evaluate the iterated integrals J. J. p2 cose dr de̟ A 1 В) 2

A: ddθ(sinθ)=cosθ ∫rndr=rn+1n+1, for any real number n.

Q: Use an iterated integral to find the area of the region. dy dx = y 81 7 5 4 3 2 1- 1 2 3 4 6 8

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Q: Find the area of the region enclosed by the curves y = x² and y integrating with respect to y. = 6x…

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Q: Determine which value best approximates the area of the region bounded by the graphs of f and g.…

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Q: Evaluate the iterated integral. NOTE: Enter the exact answer. yz dx dz dy : -54 -36

A: Triple integral

Q: Represent the plane curve by a vector-valued function

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Q: a 0 0 0 0b0 0 0 0 c 0 0 0 0 d Using cofactor method, prove that det M = = abcd

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 1. Find the equation of the tangent line to the curve x = e', y = et at t = 1.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Question 6 Use double integration to find the volume of the solid. ... 3 3x + 2y + 4z = 12 A) 6 B) 9…

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Q: Evaluate JJ xy dA, where R is the region in (1, 3) (5, 3) (2, 1) (4, 1)

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Q: ||r'(t) x r"(t)|| Use the formula k(t) to find k(t). 13 r(t) = t’i+t5j K(t) =

A: We have to find k(t)

Q: Calculate the (f(g(x)))' and (g(f(x)))' derivatives if f(x) = x8 1 g(x) 5x + 1 (Express numbers in…

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Q: Find the length of the curve, L. y² = 4 (x + 5)* , 0 0

A: To find the length of the given curve

Q: Question 2 Use double integration to find the volume of the solid bounded by the paraboloid z = 9x2…

A: