Let F and G be vector-valued functions such that F(t) = (cos(nt), e²t-1, t² – 1), Ġ(1) = (1, 1, – 1), Ğ'(1) = (2,3, 2), Ğ"(1) = (0,1,0) i. Find a vector equation of the tangent line to the graph of F at (-1, e, 0). ii. Evaluate (F · G)'(1). iii. Evaluate (G x G')'(1). %3D

Q: X 1 (A) If g tan , find the derivative 1² +2 yz of g at point (1,2,-1) in the direction of the…

A: Directional derivative of the function

Q: Determine f g a) f(t) = cos(t), g(t) = t b) f(t)=e¹, g(t) = e' sin(t)

A:

Q: Find f.  f''(t)=sin t + cos t,    f(0)=2,    f'(0)=4f f(t)= ?

A:

Q: Find y as a function of a if y(0) = 7, y'(0) = 4, y"(0) = 133. y(x) = y" - 8y" -y + 8y = 0,

A:

Q: Find F(t) such that F'(t) = sec³ (t) tan³ (t) and F (3) = 0.

A:

Q: Find y as a function of a if y(1) = 3, y'(1) = -7. y = r²y" + 3xy' - 63y = 0,

A:

Q: 6. Use a property of derivatives of vector valued functions to show that # [F(t) × F'(t)] = F(t) ×…

A: to show ddtrt→×rt→'=rt→×rt→'' we will use  ddtu→×v→=u→ddtv→+v→ddtu→

Q: apply property of differentiation of laplace in the equation f(t)= t cos 2t and f(t)=t^2e^-3t

A:

Q: apply shifting property of laplace in the equation f(t)= t cos 2t and f(t)=t^2e^-3t

A: To apply the shifting property of Laplace in the given equations.

Q: The directional derivative of f(z, V, z) =y-vz at the point (2, 1,1), in the direction of the…

A: We have to find directional derivative of given function f in the direction of tangent line of the…

Q: Find the direction field for the equation: y' = x + sin(y) + cos (x) at the point A = (0, pi3)

A: The direction field also known as slope field is used to graphically represent the solutions of…

Q: Find y as a function of a if y(1)9, y'(1) = -5. y = x²y" - 15xy' + 64y = x²,

A:

Q: Finf the equation of the tangent line to (cos(x)ex10x)/(Sec2(5x)+1)+11 at the point (0,11)

A: Given,           The equation of the tangent line to (cos(x)ex10x)(sec2(5x)+1)+11  at the point…

Q: Suppose the velocity of a ninja is given by v = ft, 3t², sin(π) at time t. If the position of the…

A:

Q: Find the x and y coordinates on the graph of f (x) = x³ - 3x where the tangent is horizontal. (A)…

A:

Q: Apply the first part of the fundamental theorem to determine the value of F'(x) if: e) F (x) = S…

A:

Q: e) s = cos (1– 21) -2 4t f) y = t+1, .2 x + x g) y =

A: