A point is moving along a curve that is given as: R() = (cos 31)i + (sin 31)j + (3r)k. Find: a) The derivative of the function f(x, y, z)= xyz in the direction of the velocity vector of the given curve at 1¹= π/3. b) How far does the point travel along its path from t= 0 to t = 2m.

Q: Find an equation of the tangent line at the given point on the curve. (a) x = 2 – 3 cos 0, y = 3+ 2…

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A: Let us consider the given curve r(t) the tangent line is obtained as Find the derivative of the…

Q: 1. Find the first derivative of the given function given. a. y = sint cos t b. y = 6 tan(2n + 3x)

A: In this question we have to find the first derivate of the given function.

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A: rs=s, 2s, s2

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Q: . Determine the derivative of the following complex functions: f(z) = (z³ + 3z²)³at z = 2i b. Item…

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Q: Find the equation of the tangent line of the curve y = sin r + cos a at the point A(, v2).

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Q: 4 (t) = -5 sin t + 8sec?t – 8 csct cot t + 4et + - 1+

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A: dsintdt=costdcostdt=-sintdydx=dydtdxdt

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Q: '] Find the derivative of the function. a) y=c sint+\t cos t b) y = secx+e

A: Tje solution of the problem is given in the next steps .

Q: Find the equation of the line tangent to the cardioid r = 1+ sin(0) at Ô0 =

A: Given that,, Here, differentiate w.r.t. ,we get, We know that, To find: equation of the line…

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Q: 24. A point is moving along a curve that is given as: R(!) = (cos 3!)i + (sin 31) j + (31)k. Find:…

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Q: sin 0.5 va Find the first-order derivative of y = at x = 2 and h = 0.2 a.) Forward difference b.)…

A: Three approximations to the derivative of function f(x) at x=k are 1.  the one-sided (forward)…

Q: (b) Find the derivative, d af sin dr sin (vt) dt.

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A: Slope of tangent is equal to dy/dx.

Q: Find the derivative 1 R(t) = 2 sin(t)- 4 cot(t) %3D

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