IV. Let F be a vector-valued function such that 1 F¹ (1) = '1 + 12,31² and F(0) = (-1, 0, -2). 1. Determine F(t). 2. Find a vector equation of the line tangent to the graph of F at t = 1.

Q: 1. Let ř(1) = . Find a vector and parametric equation of the line tangent to F(1) at the point (-…

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Q: Find a equation vector and the equation of the tangent line at the point P0 where t=0.2 on the graph…

A: The tangent is the line that just touches the curve at the point. The equation for the tangent line…

Q: R(t) = = {{In(3 In(3 – t), (0, -1, 4), 4t-8 4-t2⁹ 8), 3t² – 8 t#2 t = 2.

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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: #3. Consider the function xy2 if (x, y)# (0,0), f (x, y) = {x2+y2 if (x, y) = (0,0). Calculate the…

A: Given function is fx,y=xy2x2+y2if x,y≠0,00          if x,y=0,0 We have to calculate the directional…