Find the derivative of r1(t) = < 2t^2,3t,4e^2t > and r2(t) = < 5t,3,sin(t)> A) find r1(2) B) find the parametization of R1(2)
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Find the derivative of r1(t) = < 2t^2,3t,4e^2t > and r2(t) = < 5t,3,sin(t)>
A) find r1(2)
B) find the parametization of R1(2)
Step by step
Solved in 3 steps
- Find the unit vectors that are parallel to the tangent of the polynomial y= x^3 +2x + 1 at the point (1,4)4 Find the directional derivative of f (x,y)= 2x^2 y^2 -3xy at the point (1,-1) in thedirectiona. of vector v =<4,3> and toward the origin.Find the domain of the vector function r(t) = (sqrt(25-t^2),e^(-2t),ln(t+3))
- Let vector r(t) = <5sin(t), 5cos(t), 2t^(3/2)> be the position function of an object.a. Find vector v(t) and vector a(t), the velocity and acceleration of the object.b. Find the speed of the object.c. Find the distance the object travels on the interval [0, 1]. Also find the average speed of theobject on this interval.Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The paraboloid z = 3x2 + y2 and the parabolic cylinder y = 2x2 r(t) = (1,322 + 9^) * Need Help? Read ItCalculate the derivative (r × r'), where r = (5t, t²,e¹). dt (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) d (rxr') = (2te',-5e¹,0) dt Incorrect
- VECTOR DIFFERENTIATION: If d(^2)A/dt^2 = 6t i - 24t(^2)j = 4sintk, find A given that A = 2i + j and dA/dt = -i – 3k at t =0.Eliminate the parameter t to find a Cartesian equation for: x = t^2 and y = 3 + 1t and express the equation in the form x = A(y^2) + B(y) + CEvaluate the directional derivative of the function f=x^2-y^2+2z^2 at the point A (1,2,3) in the direction of the line AB where B is the point (5,0,4).