Find the Torsion along the curve: X = (t-sin t)ê +(1- cos t)ê, +tê,. %3D

Q: 1 Use the Trapezium Rule, with seven ordinates, to evaluate In(sin.r+3)dxcorrect to four decimal…

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Q: Cary)= x°Cscx +secy J sinx Cot y

A: Given function is fx, y =x3 cscx +secy sinx coty

Q: dy Find for the curve: x dx :4 cos t, y = 16 sin t, 0<t < 2T

A: We have to find dy/dx for the given function

Q: curve ï = 3t — 5, y = 4t +6 with 5 ≤ t ≤ 6.

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Q: For r=1+2cos(theta) Determine the points where the tangent line is vertical, By finding the angles,…

A: We will use integral to find area and arc length of polar curve  Note: maximum 3 subpart are allowed…

Q: Fineling the derivative of trigonometric %3D

A: Given:  f(x)=ln(2+x )

Q: x = 2 sin-1 1, y = In (1 – r²) (0<1s!)

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Q: Sketch the given curve: R. (t) = (3 cos t, 4 sin t), 0 ≤ t ≤ 2m.

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Q: dy Find for the curve 49 + 6x° = 3 + sin(7x-y). da

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

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Q: Q2: a) Find dy/dx for xy cot(xy)?

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Q: F(t) = %3D a. elliptical helix |F(t) = b. conical helix %3D ]F(t) = c. line d. circular helix…

A: We will use standard parametric form of these curve to match   For circle x = a cos(t) y = a sin(t)…

Q: find enclosed by following curves area Oくx(2て (a) 4= Cog x ;y=2- Cosx ; (b) y = X Sitx? Recall…

A: (a) y=cos(x), y=2-cos(x) Lets graph both equations using graphing calculator Area =∫abupper…

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

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Q: Find ſo F · dr for F = 8yi – (sin y)j on the curve counterclockwise around the unit circle C…

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Q: Q: Find the condition that the line x cos a +y sin a = p may touch the curve x"y" = a™*".

A: Answer

Q: dx = ( sin 2y – 2x cot y) dy is ? -

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Q: Find the length of one arch of the cycloid x = 5(t – sin(t)), y = 5(1 – cos(t)). %3D Check Answer

A: The given parametric equations are: x=5t-sint, y=51-cost The formula of the length of arch S is…

Q: dy : Find for y = cot (4 – 2²). da

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Q: y = sec ² t 2 y=1-₁² 0 t

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