Find the second derivative of the vector-valued function F(t) = (6t+3 sin(t))i + (3t + 4 cos(t))] 7"(t) =

Q: Find f. f "(x) = 7 + cos(x), f(0) = -1, f(7x/2) = 0 %3D %3D f(x)

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

Q: Find f if ƒ"(t) = 2et + 3 sin(t), ƒ(0) = 2, ƒ(π) = 5. f(t) =

A: f''( t ) = 2et + 3sint f( 0 ) = 2 f( π ) = 5

Q: Find f. f(0) = = f"(0) = sin(0) + cos(8), f(0) = 3, f'(0) = 2

A: f"θ=sinθ+cosθ Integrating both sides  ∫f" θdθ=∫sinθdθ+∫cosθdθ f'θ=-cosθ+sinθ+C..... (i)  Put θ=0…

Q: Find f. f(t) = f"(t) = 7et + 3 sin t, Need Help? Read It f(0) = 0, f(π) = 0

A:

Q: (c) Compute the derivative of u = Vt² +2vt³.

A:

Q: Find the second derivative of F(t) = | sin(x) cos(2)d.r.

A:

Q: Calculate the derivative of t2 -k 3 - t F(t) = cos(t) i + 3e2t+2j + |

A:

Q: Find F(s). F(s) = L(1 et + 3e-4t) cos(2t)} -

A:

Q: Let f (t) = e7t sin 8t Find L{f' (t).}

A:

Q: Find f. f"(0) = sin(0) + cos(8), f(0) = 5, f'(0) = 2

A: Given, f"(θ)=sinθ+cosθ f(0)=5 and f'(0)=2

Q: Calculate the derivative of the function. Then find the value of the derivative as specified. 6. V12…

A:

Q: Find f. f "(t) = 2et + 5 sin t, f(0) = 0, f(x) = 0 f(t) =

A: We can solve the given problem using the concept of application of integral.

Q: -E (B₁ Cos 2t + B₂ Sinat) é e fit) = 122+ (B₁ Cos 2t +

A:

Q: Find f. f(t) =|| f"(t) - 3et+ 5 sin t, f(0) = 0, f(T) = 0

A: To find f.f''t=3et+5 sin t, f0=0, fπ=0

Q: f(z) = 3z° cos(z) f'(z) =

A: To find f'(x)

Q: 9a) Find the local extrema of the function f(x) = e*(x² -3) using the Second Derivative Test.

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:

Q: Evaluate r(2) and r(-1) for r(t) =(sin~ t, t 2, (t2 + 1)- 1 ).

A: Given:rt=sint , t2, t2+1-1

Q: Find f. f"(t) = 5et + 4 sin t, f(0) = 0, f(1T) = 0 f(t)

A: topic- differential equation

Q: Let f"(t) = 2t + sin t, f(0) = 1 and f'(0) = 2. Evaluate f(27).

A: