Calculate[ri(t) r2(t)] and [r₁(t) × r2(t)] first by differentiating dt the product directly and then by applying the formulas d ri(t) r₂(t)]=r₁(t). + r₂(t) and dr2 dri dt dt dt dr₂, dri =[r₁(t) × r₂(t)] = r₁(t) × + × r₂(t). dt dt r₁(t) = 7ti + 9t²j+5t³k, r₂(t) = t¹k d tri(t) r₂(t)] d dt [ri(t) × r₂(t)]:

Q: s(t) = (3t1/2+2)(5t1/3+1). Find the derivative of the function using the product rule and simplify…

A:

Q: Consider the function Compute f"(x). X = 66²⁰ - f(x) = -3t²- f"(x) = -4t+ 3 dt.

A:

Q: Calculate r' (t) and T(t), where r(t) = (2t - 7,2 – 5t, 3 + 5t). r' (t) = (2 T(t) = -5 5

A:

Q: 4 3 2 1 y 1 y = f(x) 2 3 4 -X

A:

Q: Calculate the linearization L of f(x) : 5e* at x = 1. x2 Express your answer in terms of e and x.

A:

Q: Let D, be the linear transformation from C'[a, b] into C[a, b). Find the preimage of the function.…

A:

Q: f (x) = x2 – 2x + 2 | P 3 3+h an expression for the gradient of the line joining the points, P and…

A:

Q: Find the linearization L(x) of the function f(x)=x to the 4th power +2x to the 2nd power +1 at x=2.…

A:

Q: Example. 4.8 A tank contains 300 litres of fluid in which 20 grams of salt is dissolved. Brine…

A: Given, At initially the tank contains 300 liters of fluid in which 20 grams of salt dissolved. And…

Q: Use the quotient rule to find the derivative of 3w + w4 R (w) = %3D 2w2 + 1

A:

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) × r"(t). P(C) = 21²1 - 48 + ²P²H 2³k r(t) 3 (a) r(t) 3it…

A:

Q: Differentiate the function. = In({ (4t+ 1)³ (4t-1)5 F'(t) = F(t) = In

A: The derivative of the function in the division form is given by the quotient rule which is given by-…

Q: Differentiate the function. r(t) = (3²- + 8)i + r'(t) = (6t)i + ( 132 r'(t) = i + (6t)j r'(t) =…

A:

Q: Determine the variation of the functional (b) J(x)=√ [x7(1) + x₁(1)x₂(1) + x3(1) + 2x₁(1)×₂(1)] dt.

A: To determine the variation of the functional J(x), we need to find the variation δJ for an arbitrary…

Q: F = (2+-1) dt

A:

Q: Use the Fundamental Theorem of Calculus Part I to find dh/dx given h(x) = cost dt (Hìnt: need…

A: Answer:  By fundamental theorem of calculus  Let fx=∫axbx gt. dt   dfdx=gbx.b'x-gax.a'x

Q: For the function z = - 8x³ - 2y² - 2xy, find a z(1,-2), andz(1,-2). dz dz a ax' dy ax

A:

Q: A non-linear function is given by f(z) = a²-1 Where a is a constant. a) Obtain the linearized form…

A:

Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

Q: Find the linearization L(x) of f(x) at x = a. f(x) a = 0 %3D 7x +4 L(x) 16 ** 16 L(x) 16 4. 7 L(x) =…

A:

Q: = 4+ J₁ Find F'(x). 2t² + 1 t² + 3 dt.

A: