find Laploce trans form of function f (t) =t et (Sinh 3t - 7t )

Q: Find an equation for the line tangent to the curve at the point defined by the given value of t. x-…

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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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Q: Let y = tan(5ax + 5). Find the differential dy when x 3 and dx 0.2 Find the differential dy when x =…

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Q: Find the differential of each function. (a) y = tan(7t) dy = 3 - v2 (b) у 3 3 + v2 dy =

A: topic - differential equations

Q: Find the length of the curve y = In sin x from t = -2 to t = 0.

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Q: Let y = tan find the differential dy of the function.

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Q: Find the point on the curve r(t) = (5 sin t)i + (5 cos t)j + 12t k at a distance 26p units along the…

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Q: Find the extremal of the functions using Euler's equation. [²(x² + y² (y2 + y² + 2ye*)dx, y (0) = 0,…

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Q: | t sin(2t) dt 1.

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Q: 1: A)find the length of the curve y=3(x)/2 – 1 from x=0 to x=1 ? B) Prove that: cosh (x + y) = coshx…

A: A) Length of the curve is y=3x32-1 B) Trigonometric function

Q: Q7) Set up the integral representing the length of the curve (sint, cos² t), cos"e). - – s1s. <t< 2

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Q: f (t) sinh 3t + cosh 3t 2t3 -

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Q: Find G(1), G'(0), and G'(π/4), where G(x) =

A: Here we have;  G(x)=∫1xtant dt

Q: If the PSD of X(t) is S„(@). Find the PSD of dX(t) dt

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Q: Find cosh² (t) sinh5 (t) dt.

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Q: Find the differential of the function. y = 0 sin(60) dy =

A: To find the differentiable of the below function. y=θ3sin6θ

Q: F(t) = arcsin(In(t)) · arctan(3t²) – arccos(/2).

A: Given data:   The given expression of the the function is:…

Q: Let y = tan(5x + 2). Find the differential dy when x = 4 and da = 0.3 0.6 Find the differential dy…

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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: Find the length of the curve y = ln sin x from t = −2 to t = 0.

A: f(x)=y=ln(sinx) Arc length =∫ab1+(f'(x))2dx f'(x)=dln(sinx)dx=1sinxdsinxdx=cosxsinx=cotx a=-2 b=0

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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Q: Find the speed (as a function of t ) of a particle whose position at time t seconds is c(t) = (sin t…

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Q: Sketch the curve. And indicate the direction of increasing T at T =0

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Q: Find the differential of each function. (a) y = tan 7t dy = %3D 5 - v2 (b) у%3D 5 + v? %3D

A: we have to find the derivative of the following

Q: d cosh z =sinh x dz صواب ihi

A: Use the formula of coshz and sinhz in terms of exponents.

Q: Find the length of the curve. x = cos t y = sint 0 <t< 2n

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Q: 8. Find the length of the curve defined by x = cos(2t), y = sin(2t) from t = 0 to t = n.

A: If x = f(t), y = g(t) in (a, b) then length of the curve is,

Q: Find the differential of each function. (a) y = tan(3t) dy =

A: We have given  y= tan(√3t)  We have to find the differential equation.

Q: Find the differential of each function. (a) y = etan(nt) tan(at) · soc2 (at) - T dy = sec“(at) · T e…

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Q: a(22) V17 – cos(2nt)" (2 – 4) sin() 1. Given f(x) dt, find the equation of the line tangent to the…

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Q: Q1. Find the length of the of the curve y = In(cos x) from x = 0 to x = 4

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Q: 1. Determine the equation of the tangent line to the graph of f(a) = [² pr+sin r = x = 0. cos (t² +…

A: Above equation of tangent is given.

Q: curve at the given point. Jx = 1? – 2 7. at (-1, 0) ly=t -1 at (-1,0)

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Q: (il) Find the point in which the tangent line to the curve F-12-30)1+ 2+Int'+ k at t=1 intersects…

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Q: dy Find for the following function de sin 0 y : ACos 0-1.

A: We have to find derivative

Q: Express x = ln(7t), y = 9-t in the form y = f(x) by eliminating the parameter.

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Q: 13. F(x) = sin t dt 20

A: We need to definite integral properties  also integral of sinx is -cosx

Q: . Let y =sqrtx Find the differential dy

A: To find, y=x To find the differential dy.

Q: e) Differentiate f (t) = (e-6t+ sin(2-t)) -9- %3D

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Q: Determine the length of the curve TC f(x) = In[sec(x)],0 < x < 4

A: The given curve is- f(x)=lnsec(x)Interval 0≤x≤π4We need to determine the length of the given…

Q: Find the exact length of the curve. y = (x-x2)1/2 + sin-1((x1/2))

A: The arc length formula is given as

Q: Use Taylor's formula to find a quadratic approximation of f(x,y) = 9 cos x cos y at the origin.…

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Q: Let f(x,y) = tan 1(sinh (y) + 2020 cos - 'y) + 4xy Calculate

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Q: Find the differential of each function. (a) y = tan 3t dy =

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Q: Find the differential of the function. y = 6 sin(60) dy

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Q: Find the differential dy of the function y = 4 sin (2x). Provide your answer below: dy=dx

A: Solution

Q: Find an (1,1) equation of the tangent i ine at the curue yt+xy = x_x+a. on

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Q: 7) Let x = t – sin(t) , y = 1– cos(t). Determine the equation of the line tangent at t = n.

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