Find an arc length parametrization r(t) = (e¹ sin(t), et cos(t), 7eª). Assume t(s) T1(s) = (0) = r₁(s) of 0 when s = 0, and t'(0) > 0.

Q: Find the following for the given equation. r(t) = (e-t, 5t², 7 tan(t)) (a) r(t) (b) r"(t) = (c) Find…

A: Given: rt = e-t, 5t2, 7 tan t To find: r't , r''t and r'(t)·r''t We know that  ddxex = ex ; ddxtanx…

Q: Find '(t), given r(t) = (-4e-²t, 4t² + 3, 3 sin(−3t)). r' (t) =

A: Given vector is as follows

Q: Let r(t) = (sin t, 2 cos t), t = (a) Find r'(t). (b) Find T(t).

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Q: Let ro)-플-x a-글 FW) = b = 0, and n=3. Then: cos (f(x))dx =

A: We can find the integration as below

Q: (1) Find and classify the extremes value of f(x) = 6x* – 4x° over the interval [-2, 2). (2) A…

A: According to Bartleby Q/A guidelines, we only allow solving the first question if multiple questions…

Q: 3. g(t) = arcsin (E - find g'(t) A. (4-t+) В. (4-t+)ž C. - 2t5 (4-t4)ž 2t D. (4-t+)5

A: 3-Given- gt=arcsint22-t24-t4 To Find- The value of g't.

Q: Let ƒ (t) = e5t sin 7t. Part (a) Find L{f (t)}. Part (b) Find L{f' (t)}.

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Q: Find T, N and B for the curve 7(t) = (4 cos(2t), 4 sin(2t), 2t) at the point t = 0 %3D Give your…

A: given that                                          r→(t)=4cos(2t), 4sin(2t), 2t at t=0…

Q: Suppose that r(t) =. Then the speed is

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Q: A particle is moving along the path given by R(t) = (sin(ln t), cos(ln t), √√3 lnt). (a)…

A: Introduction: The formula of arc-length of the polar curve from a to b is given by,…

Q: ind the length of the curve x cos(t) + In(tan(;t)), y = sin(t), /4<t< 3n/4. %3D ength =

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Q: Q. Suppose a vibrating string is governed by the equation f (x, t) = 2 cos(5t) sin x, where x is the…

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Q: of dx- = 0, then dy |=0. Prove that is a function f is harmonic

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Q: Find the length L of the curve R(t) = e" cos(2t) i + e* sin(2t) j+2e"k over the interval [1, 4]. L =

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Q: Consider the curve where a is the last digit of your exam number. (a) Compute=7 (t) at t € [0, +∞).…

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Q: Find f. f "(t) = 2et + 5 sin t, f(0) = 0, f(x) = 0 f(t) =

A: We can solve the given problem using the concept of application of integral.

Q: A yoyo bounces up and down in the vertical direction with its acceleration after tt seconds given by…

A: d^2y/dt^2 = a(t)

Q: d (h) Find sec (arctan (0~))] do

A: We need to find out the derivative.

Q: Find f. f(t) = 5e¹ - 6 sin(t) — 5 f"(t) = 5et + 6 sin t, f(0) = 0, f(π) = X 0

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Q: The slope of the tangent line to the curve parametrized by the equations x (t) = -2(cos(t) + t…

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

Q: Consider the curve defined by r(t) = (cos(t) + t sin(t))+ (sin(t)- t cos(t))] for t > 0. (a) Compute…

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Q: 7) Determine an eq ,in (x) and (y) , and then find a) y sec 1t , x csc-1t b) y = (sin 0)* ,x = (cos…

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Q: Determine un ju should be a plane curve. ion f (0) so that x = a cose, y = a sin0, z = f (0)

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Q: a) y = 1 √x - √x²+4+tan().

A: To find the derivative of given function