1. When is the object at rest? Your ansiôier

Q: Find the points on the cardioid r = 1−cosθ at which there is a horizontal tangent line, a vertical…

A: Consider the given: r=1−cosθWrite the cartesian…

Q: a.) Evaleiate. (6tanx dx

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Q: Find the arclength of y = 2x + 3 on 0 < x < 3

A: Find the differentiation of the function and then substitute the function in the arc length equation…

Q: WATE [z cot FI dz

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Q: Eliminate the paranoter t from the follewing S r(1) = 4+ sin t lu(t) 3- cost

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Q: 63; Evaluate the întegral +3 dx + 6xy dy where Cay Curve Joininy (t, -) to (16, I),

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Q: Find the first and second deriva tives sp dt

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Q: can any thing said about the tengent to the curves y=sinmx and y= - sin(x/m) at the origion (ma…

A: Solution  Given

Q: what would be the inebriation of the figure below after a reflection across the x-axis?

A: We have to find the reflection of the given figure accross x axis.

Q: Find the length of the curve over the given interval. r = 4 sin θ, [0, π]

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Q: Find equations for the tangent and normal to the cissoid of Diocles y2(2 - x) = x3 at (1, 1).

A: Find dy/dx using the given equation.

Q: Find the arclength of y = 4x - 2 on 0 < x < 1

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Q: find y'' for the curve cosx-siny=4

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Q: 2, The hadiusS r of a sphere is increasing as a vate af 3amimin. Find the rate af Ghane e Of Ahe…

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Q: If h(z) = arcsin(2)(4z + 3), find h'(z) =

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Q: Given show =5 how dy %3D

A: differentiate y with respect to x .

Q: 3. Find the area under one arch of the curve y = sin(2r).

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Q: (a) (., Consider the curve defined by ry = In(3x + sin(y)). Use implicit differenti- ation to find…

A: Consider the given equation of the curve, xy=ln3x+siny Use the implicit differentiation,…

Q: Use trapezoidal with 3 level Romberg ( k=3) to evaluate 1 Пх - Пх* cos dx 4

A: The complete solutions are given below

Q: / Does the following equation satisfied Cauchy-Riemann's equation. (w=z

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Q: a. y = cot¯(Ve") tanh(e") -1

A: Since you have asked multiple questions in single request so we will be answering only first…

Q: Find the arclength of y = 2a + 4 on 0 < a < 4

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Q: a²z a2z If z = arctan (2), find ду?

A: It is given that z=arctanyx z=tan-1yx

Q: Question The approximation of fxln (x + 5) dx using two points Gaussian quadrature formula is:

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Q: Now, we can say that the work done in stretching the spring 15 in. = X ft beyond its natural length…

A: Convert the length 9 inch to feet. Then use the Hooke’s Law to calculate the value for k.

Q: Determine the so luti'on of the equertion: dy dx2y cot x= 1- 2xcot 2x- 2csc 2x

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Q: Use Laplace Tranformation to solve the IVP.  y'+y=tsint  y(0)=0

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Q: Show that the antiderivatives are equivalent.                                                     ∫…

A: To show that ∫3x21-x6dx = arc sin x3+C Substitute  u = x3. Then                  dudx=3x2du  =3x2dx…

Q: dz az Find and of the equation z = xy arctan ax ду

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Q: Ex. 2. Prove thät if two equal and perfectly elastic balls moving in the same direction collide…

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Q: Parametrize the following curve: y = tan−1(x2 + 1)

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Q: |A" |= |B |,implies that A=B" %3D ylgn ihi

A: Use the property of vector and their modulus.

Q: Evaluate [y cos (3y) dy

A: We use integration by parts continuously. ∫f(y)g(y)dy =f(y)∫g(y)dy  - ∫df(y)dy(∫g(y)dy )dy Also note…

Q: Find II. | arctan 4t dt

A: as per our company guideline we are supposed to answer only one qs kindly post remaining qs in next…

Q: Consider a χ2-curve with df = 16. Obtain the χ2-value that has area a. 0.025 to its left. b. 0.975…

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Q: S arctan y dy y3

A: Let's evaluate given integral.

Q: cand. find dy at

A: Given that     If y=x2 - 4x and x=√(2t2+1) We have to find dy/dt at t=√2 .

Q: Find the points on the cardioid r = 4(1 – sin0) at which there is a horizontal tangent line, a…

A: According to the given information, it is required to determine the horizontal tangent line,…

Q: Evaluate the intergral attached as an image with the question.

A: The given integral is,

Q: Find the exact length of the curve. y = 2 In(cos (÷)) Tt/3 < x <T/2

A: Here given Differentiate the given function with respect to x using the chain rule of derivative

Q: Integrate counterclockwise around the unit circle (|z| = 1) and choose from the options below that…

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Q: if t(い) = ta Cosy V = X siny Determine JR ļ JR to つメ

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Q: What is the integrating foc tor of the equation %3B

A: Topic:- differential equations

Q: Determine the speed (in meters per second) of a particle with a trajectory (2 sin (3t), 9 cos (3t)),…

A: Consider the given parametric equation of the trajectory of the particle, 2sin3t,9cos3t so we can…

Q: tan What is the exact value of sc wdw ialuulexalu fXis thrali

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Q: AT is tangent to oG. 8 10 Find: AN. AN = %3D units

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Q: olve ædy = y(1+ In y – In a)

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Q: \ Compute dx using the (a) Trapezoidal rule

A: 6.(a)  Given function is ∫-11e-x2dx Trapezoidal rule ∫abfxdx≈∆x2fx0+2fx1+2fx2+2fx3+........+fxn…