The position of a baseball (in ft) is represented by r(t) = 55/2ti + (4 + 55/2t- 16t2)j. Find the arc length of the %3D trajectory (flight) of the baseball. (Let t = 0 represent when the ball is hit, Let j = 0 be ground level. Round your answer to one decimal place.) %3D Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 2 cos(t)i + 2 sin(t)j, t=

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A: Part d,Given,           lx=tanh-1x+ln1-x2To find : Find the derivative of the given function.

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A: The equation in slope intercept form is given by:y=mx+cwhere m=slope, c=y-intercept

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A: Explained below

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A: see below the answer  and calculation

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Q: Calculate the Taylor polynomials T2 and T3 centered at a = 0 for the function f(x) = 11 tan(x). %3D…

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Q: Given a function f(x,y) = x* + 2y+ 8xy - 7 The critical points of f(x,y) occur at the points P(0 ,…

A: Let's find.

Q: 1. Differentiate each function. Simplify as much as possible and express all answers using positive…

A: a) h(x)=x37xDifferentiateh'(x)=3x27x+x37xln(7)

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Q: For numbers 17- 20, use the given function. (5 + 2x, x <- 6 f(x) = } x +5, x 2- 6 17. What is the…

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A: First we find unit vector of v.

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Q: Use the graphs to evaluate the expressions below. fx) 5- 8(x) 5- 4- 4 3 -1 2 4 5 6 -1 2 3 4 5…

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Q: Find the equation of a curve going through the point (3, 7) and having slope 4x² – 3 at (x, y).

A: Given ,Slope of curve is 4x2-3Thereforedydx=4x2-3Taking integationon both…

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Q: 4 d) En=2n-1 4n2 e) 0 En=1 n2+1 4 f) En=2 n2-n (Use partial fraction decomposition)

A: Explanation of the answer is as follows

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Q: _2 .2 y = у — 2х* + 3x — 4х, у — х* Find the area of the region enclosed by the two equations. (make…

A: the region is bounded by y=2x3+3x2-4x, y=x2

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