Calculate the velocity, speed, and acceleration of the given paths. (a) x(t) = (t sin(t), t cos(t), t2) %3D (b) x(t) = (e', e2t, 2e*) %3D

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: Suppose that a boat is positioned at the origin with a water skier tethered to the boat at the point…

A: given thatThe boat trawelled along the path y=fx and passes through 19,0solution ;if…

Q: Find an equation of the tangent to the curve at the given point. x = cos(t) + cos(2t), y = sin(t) +…

A: NOTE: Refresh your page if you can't see any equations. . take derivative put the value of t

Q: : )-+(÷), zw= (C) dx 1 et %3D dt 1 (: :)-+(-), -= (C) dx dt 1

A: Given dxdt=0110 x +ete-t Here let take A= 0110A-λI=-λ11-λ=0λ2-1=0λ=±1 Hence the eigen vector for 1…

Q: 1.) Find the derivatives of a.) y = 3e²x — 2lnx + arcsec x

A: the given equation is

Q: 1) Find an equation to the line tangent to y = (x – 3) 2 at x = 0.

A:

Q: 8) Given the function y =x – 3x+1 dy Find the derivative, dx

A: Solve by derivative of given function

Q: 3) Find an equation of the tangent line to the graph of y = (z + 4)² at z = 4.

A:

Q: Consi ider the ellipse 4x² + 2xy + 5y² The derivative = d on this curve is

A: Given: 4x2+2xy+5y2=149

Q: Find derivatives of: 1.) f(t)= 7t          2.) g(x)= 3x-9      3.) h(v)= v3 4.) m(x)= π2

A:

Q: Find an equation of the tangent to the curve at the given point. (1) X²+4xy-y²-4x=1, (1,2) (2)…

A:

Q: Let the position at time t seconds of a particle moving in a coordinate line be given by s(t) =…

A: Formula used:

Q: d {(1 — 2г + 3а4)7)} dx

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 3. Find the derivative of h()= 5²°-2z-1 %3D

A: We have to find derivative

Q: Question 21 Find the equation of the tangent line to y = x = 1. at A y - Vi = - Vi (x – 1) B VE (x -…

A: