Find the vector equation of the tangent line to the curve given by 7(t) = sinti + cos (2t)j + tan tk at t = T. A. F(t) = (1, 1, 1) + t(-1,0, 1) В. F(t) = (0,0, 1) + t(-1,0,1) С. F(t) = (1,0, 0) + t(-1,0, 1) D. F(t) = (0, 1,0) + t(-1,0, 1) Е. none of the above

Q: Find the directional derivative of f(x, y) = exy in the direction u = (,) at (xo, yo): (0,1). 3545…

A: Given query is to find direction derivative.

Q: Find the equation of the tangent line to sin (x – 2y) = 2xy – 1 2лу — (1.:) at the point ( 1,

A:

Q: Find an equation of the tangent line at the given point on the curve. (a) x = 2 – 3 cos 0, y = 3+ 2…

A:

Q: Find the directional derivative of the function z(x,y) = ln(xy²) + sin(x - y) at the point…

A:

Q: Consider the curve given by the equation eªy + x² cos y cos y = 3x - y +2. 0). Find y/(0) (i.e. the…

A:

Q: What is the point of intersection of the tangent lines to the curve r(t) = sin(πt)i + 8sin(πt)j +…

A: Let us consider the given curve r(t) the tangent line is obtained as Find the derivative of the…

Q: How many horizontal tangent lines does the curve parametrized by the equations z(t) =-4t-1,…

A: on doing derivative we get the 1

Q: Find the equation of the tangent line of the curve y = sin r + cos a at the point A(, v2).

A:

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

A:

Q: Find the equation of the tangent line to the curve (a lemniscate) 2(x + y°)´ = 25 (x² – y²) at the…

A:

Q: Find the equation of the parabola whose axis is vertical and passes through (-1,0), (5,0) and (1,8).

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the derivative of r(t)=(5-1³) î+2te¹¹ ĵ+sin 31 k and find the unit tangent vector at the point…

A:

Q: 24. A point is moving along a curve that is given as: R(!) = (cos 3!)i + (sin 31) j + (31)k. Find:…

A:

Q: Determine the intersection point of the lines tangent to the curve r (t) = (senπt, 2senπt, cosπt) at…

A: The given curve is rt=sinπt,2sinπt,cosπt. Differentiating it with respect to t:…

Q: The slope of the tangent line to the curve parametrized by the equations x (t) = -2(cos(t) + t…

A: Slope of tangent is equal to dy/dx.

Q: u(x, y) = arctan a = (-1,0)

A:

Q: Determine the equation of the tangemt line to c(z) = cot (Tz)sin-1(z) at the point where z=1/2.

A: