aluate the arc length integral s(t) r(t) = (8t + 9, 3t+ 6, 4t) - symbolic notation and fo - Su 0 r'c

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A: Given

Q: The motion of a mass on a spring is described by 3y" + 4y = 0, y(0) = 5, y'(0) = 6. What is the…

A: Given:The motion is described by 3y''+4y=0, y0=5, y'0=6. We have to find the amplitude of the…

Q: differenetiate parametrically to find dy/dx in terms of t:  x=1/t+1 , y=2t^2-4

A: please use according to form i did solved two equation because your question is not write clear that…

Q: Find the length of the curve x = e' cos(t), y = e' sin(t), 0 <t < r. Length =

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Q: sin t dy If y = tan" ), show that cos t-1 dt 2 II

A: Formula Sin2x + cos2x =1  Find dy/dt

Q: Exercises 7 Evaluate: 2 (2x - 3)* dx 5 (2) J 1 dx 0*+3 (3) dx x + 9 x In x dx

A: Find the definite integral

Q: differentiate the follouwing 243 a) f(x)=2x°-in/x|+3 arccos (X)

A: Since you have asked multiple questions in the same request, as per the policy, only the first…

Q: Consider y=(x2+1)2x a) find dy/dx b)Evaluate y'(1)

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Q: f(x) = arctan( 2x) + arccos x find f'(0) 3- O A) 2 O B) 0 C) -1 O D) -2 EL 1

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Q: Compute the area bounded by the cardioid r(0) =1– sin(0) on 0, Express your answer as a decimal…

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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: Use the differential dz to approximate the change in the function z (shown in the image) as (x, y)…

A: Given that:   The given function z = f (x, y) moves from the point (1, 1) to the point (1.03, 0.95),…

Q: A spacecraft has acceleration r"(t) = , initial velocity r'(0) = and initial poition r(0) = (0, 0,…

A: GIven that a spacecraft has acceleration with initial velocity r'(0) = &lt;2, 5, 1&gt; and initial…

Q: 1 = (x + ¹)² + ²2(x + 1)² (2) Calculate the arc length of y = over the interval [1, 4].

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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: (x² + y?)3/2' + (x² + y?)3/2J OVer the curve F(t) = (e' cos(t))i+ (e' sin(t))j from the point (1,0)…

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Q: Find the length of the curve r(t) = (ln(t))i + (2 t)j + (t²) k from t = to t = e.

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Q: 3. Let f(x)= :/ arcsin(t) dt and g(x)= / arccos(t) dt. 0. 0. I f'(x) g' (x) dx =? 4 - T (a) 2 - T…

A: Given Applying derivative with respect to x: Similarly: