For the given vector-valued function below, find its (i) unit tangent vector, (iii) binormal vector, (a) r(t)=3sinti+3costj+4tk (ii) principal unit normal vector, (iv) curvature. (b) r(t)=2cos÷ti+2sin=

Q: Find the maximum rate of change of f(x, y) = ln(x² + y?) at the point (-4, -3) and the direction in…

A:

Q: 6. Find the unit vectors that are parallel to the tangent line to the curve 2x3 at the point (2,…

A: The given curve is y=2x33 at the point 2,163. Calculate the unit vector that are parallel tot he…

Q: The three components of the derivative of the vector-valued function u are positive at t = t0.…

A: Given: The three components of the derivative of the vector-valued function u are positive at t =…

Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

A: The given vector is r→t=5t sint + 5costi^+5t cost + 5sintj^. To find: (a) unit tangent curve of the…

Q: State the theorem for Gradient as a Normal Vector.

A: State the theorem for Gradient as a Normal Vector.

Q: Find the directional derivative of f(x,y)=yln(x+y) at the point (-3,5) in the direction of the…

A:

Q: Find the derivative of the vector function r(t) = ta x (b + tc), where a = (-5, −1, −1), b = (−2,…

A:

Q: f(x, 3) = In(x? + Y²òf function P(3,4) at the point of i = (9, 12) Directional derivative in the…

A:

Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (cos(t) , sin(3t) , sin( when…

A: Given r(t)=cos(t) , sin(3t) , sin(t) Compare it with r(t)=x(t) , y(t) , z(t) to obtain…

Q: C- Find unit vectors tangent and normal to the curves (y=4sine x-1-3cos8) at 8=:

A:

Q: Decide if the points given in polar coordinates are the same. If they are the same, enter T. If they…

A: Question: a) (9, π/3), (-9, -π/3)  These points are different. The r-values have opposite signs,…

Q: Consider the function defined by f(x,y) = 4xy - 2x2. Evaluate the directional derivative of f at…

A:

Q: Determine the equation of the tangent plane and a vector equation of the normal line to A. tangent…

A:

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Here we use the formula, Dvf(x,y)=∇f(x,y).v

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(xy)…

A: