Find the length of the curve c(t) defined by c(t) = (-4 cos (t), -4 sin (t), t) if 0 ≤ t ≤ 2л and c(t) = (-7, t - 2n, 6t) if 2л ≤ t ≤ 4π.

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: Find f if ƒ"(t) = 2et + 3 sin(t), ƒ(0) = 2, ƒ(π) = 5. f(t) =

A: f''( t ) = 2et + 3sint f( 0 ) = 2 f( π ) = 5

Q: (a) Find the equation of the tangent line to the curvey 2 sec x- 4 cos x at the point , 2) %3D

A: Since you have posted a multiple  question according to guildlines I will solve first…

Q: Let (t) = Find '(t) '(t)=<

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Q: ind the fangent line for... 1x1) = +²+et ( (1) = sh (k) + t at t=0 B) r(e) = sinG + case at 6: T

A: Explaination of the answer is as follows

Q: #15) Determine y' a.y=sin 2x b. y = x² sinx co y = sin(-x) Determine #16.> d.) y = cos x sin x e-> y…

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Q: Let f(x) = x² + 2x+1 a) Find the equation of the secant line between the points P and Q on the graph…

A: Let (a) To find the equation of the secant line between the points P and Q on the graph of , where P…

Q: Sketch the curve r(t)=f°i+tj and indicate the orientation. Find r'(t) and sketch r(1) & r°(1).

A: First we will plot the given parameters.

Q: Let f (t) = te* +e sin 10t. Find L{f (t)}.

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Q: Let y(1) = (1/2)teit/2. 0 <t< 2n What is the terminal point of the curve? IT —2л

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Q: Find F(s). F(s) = L(1 et + 3e-4t) cos(2t)} -

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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: Find f. f(t) =|| f"(t) - 3et+ 5 sin t, f(0) = 0, f(T) = 0

A: To find f.f''t=3et+5 sin t, f0=0, fπ=0

Q: Determine the intersection point of the lines tangent to the curve r (t) = (senπt, 2senπt, cosπt) at…

A: The given curve is rt=sinπt,2sinπt,cosπt. Differentiating it with respect to t:…

Q: Suppose r' (t) = (cos(t), et, 2t) and r(0) = (1, 0, 3). Find r(t).

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Q: Find the value of the derivative dy/dx at  t=2π/3 when an object moves according to the parametric…

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Q: For the curve x (t) = t², y (t) =t³ – 3t Given the curve crosses itself at (3, 0), a) Find the…

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Q: Find T, N and B for the curve 7(t) (2 cos(2t), 2 sin(2t), 5t) at the point t = 0 Give your answers…

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Q: Q3) for f(t) = sec?(6t – 1) and g(t) = tan?(6t - 1) show that %3D f'(t) = g'(t).

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Q: Determine the equation of the tangemt line to c(z) = cot (Tz)sin-1(z) at the point where z=1/2.

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Q: Determine r (x) if r(x) = (arccot(x))".

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Q: Evaluate r(2) and r(-1) for r(t) =(sin~ t, t 2, (t2 + 1)- 1 ).

A: Given:rt=sint , t2, t2+1-1

Q: ind the equation of the curve whose y" = ○ y=2 sin-¹ (2) — 4³-√3 -1 - O y = y = sin¯¹(x). X sin (x)…

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Q: Find f. f"(t) = 5et + 4 sin t, f(0) = 0, f(1T) = 0 f(t)

A: topic- differential equation

Q: Find the arclingth of A) r(6) = 4cos (0) OS OS T ... B) / X (²) = +²+1 2 y(t) = 2³² +2 1≤t≤ 3

A: