Find the dy/dx of the parametric equations given: x= 2t² – t and y= t³ – 2t – 1

Q: A particle is moving with the given data. Find the position of the particle. a(t) = t - 8, s(0) = 4,…

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Q: Evaluate (2x - y) dx + (x + 8y) dy. C: x-axis from x = 0 to x = 3

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Q: Find T(t) and N(t) at the given point. x = e' cos t, y = e' sin t, z = t = 0 T(0) = N(0) =

A: Unit tangent and normal vector

Q: Express the iterated integral as an equivalent integral with the order of integration reversed. r36…

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Q: Question 5 Find the surface area of that portion of the surface z = V4 -x that lies above the…

A: Option (B) is correct

Q: Find the conservative vector field for the potential function by finding its gradient. h(x, y, z) =…

A: We have to find the conservative vector field.

Q: A torus formed by revolving the region bounded by the circle x2 + y2 = 49 about the line x = 8 (see…

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Q: 3. The derivative of /(x) = In x at x = 3 when hourrent = 0.001 and hprevious = 0.002

A: Given problem:- 3. The derivative of f(x) = In x at x = 3 when hcureent= 0.001 and hprevious = 0.002…

Q: 3. If f and are continuous functions with f(3) 4 and lim 2f(x)-9(r)3D5, what is g(3)?

A: To evaluate the value of the function

Q: dx 2 X + 4

A: Topic = Integration

Q: 1 Find the length of the arc of y= from x = 1 to x = 3. 2x

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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: Use the arc length formula to find the length of the curve y = 3x – 5, -2sxs 3. Check your answer by…

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Q: Use a double integral to find the volume under the plane z=38x+y and over the rectangle…

A: We have to find the volume using double integration.

Q: Question 7 Use double integration to find the volume of the solid. 3 3x + 2y + 4z = 12 A) 6 B) 9 c)…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x3 - y³, P(4,…

A: Given :f=x3-y3

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

A: Given

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

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Q: 1. Set up the following improper integrals by definition. sin(x) dx 22 — За — 4 а. xe dx с. 4 et b.…

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Q: Find V · (V × F) if F(x, y, z) = 4 sin xi + 8 cos(7x – 8y)j + zk. V: (V × F)

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Q: Find an equation of a line through the point (-1,3) making an angle of 45 degrees with the line…

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Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

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Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

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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: Find the arc length of the parametric curve. x = 7 cos(t), y = 7 sin(t), z = 24t; 0<t< T L =

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Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = xyz, P(7,…

A: To find the directional derivative of the function at P in the direction of v.hx, y, z=xyz, P7, 2,…

Q: Find the area of the region inside the circle r = 30 sin 0 and outside the cardioid r = 10 + 10 sin…

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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 curl (9z i + 10x j + 5y k). curl (9z i + 10x j + 5y k) = ( i )i + ( i j + ( i

A: Curl

Q: V4-x² c 3-x²-y² x dz dy dx J_5+x²+y² A 128/15 B 16/89 23/6 D) 6

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Q: Find the principal unit normal vectóř tô thể curve at the r(t) = /2ti + e'j + e-k, t = 0 %3D

A: Principal unit normal vector

Q: y=2\4-x²

A: Since we are given with the multiple number of question and our guideline is solve first question…

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: Question 13 2 Evaluate the iterated integral. yz dx dz dy

A: Evaluate the iterated integral .

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

A: Triple integral

Q: Sketch the region in the plane consisting of points whose polar coordinates satisfy the given…

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Q: 2. Write the given (total) area as an integral! a. The area above the x - axis and below y = 4 -x2 T…

A: Area between the curve  y=f(x) and x-axis is defined as ∫abf(x)dx where a, b are point of the…

Q: <press the area of the given surface as an iterated double integral, and then find the surface area.…

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Q: Evaluate the iterated integral. yz dx dz dy 45 в) 34 47/3 D) 5

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

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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: sine "/2 Evaluate the iterated integrals r cos e dr de A 1/6 1/2 11/9

A: Explanation of the answer is as follows

Q: Find div F and curl F if F(x, y, z) = 13y*z'i – 11a'2®j – 5xy*k. div F= curl F=

A: We can solve as follows

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: Fidn the sum: 2k (Write your final answer in fraction form, when applicable) A=31

A: Use the formula of summation then put the limits .

Q: Use the arc length formula to find the length of the curve  y = 3x − 5,   −2 ≤ x ≤ 3.  Check your…

A: Given : y=3x-5 ,   -2≤x≤3   To Find : Arc length

Q: 1- Show that the following subset is a subgroup. H = {o e S, l0(n) = n}cS,

A: We have to show given subset is a subgroup.

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

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Q: Find the curvature and the radius of curvature at the point t = 0. %3D x = e' cos(t), y = e' sin(t),…

A: r(t)=et cos(t) i+et sin(t) j+7et kr'(t)=[etcost-etsin(t)] i          +[etsint+etcos(t)] j +7et k…