d d Calculate[ri(t) r₂(t)] and [r₁(t) × r₂(t)] first by differentiating dt dt the product directly and then by applying the formulas d dr₂ dr₁ [r₁(t) · r2(t)] = r₁(t) · + r₂(t) and dt dt dt d dr₂ dr₁ [r₁(t) × r₂(t)] = r₁(t) × + x r₂(t). dt dt dt r₁(t) = cos(t)i + sin(t)j +8tk, r₂(t) = 7i+ tk d 77 [r₁(t) · r₂(t)] = = [ dt

Q: 9. f(-5) = (5)²-19 = 25 -19 -6 b. lim x²-19 X→-5 = (-5)² -19 = 25-19 = 6 с C f(-5) = lim f(x) X-7-5…

A: Solution is given below:

Q: c. y = 4e (3x²-x) C.

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Q: Sketch the region R and evaluate the iterated integral x, y) da. [²³²(¹-2x - 2x + 8y) dy dx

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Q: Determine if y=5 cos x and x=31²-5t+3 dx

A: Given,             y=5cosx , x=3t2-5t+3To find : Determine dydt

Q: Convert the point from cylindrical coordinates to spherical co (3,2,0) (p, 0, 4) = || X

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Q: The table shows a proportional relationship between the number of tickets purchase and the cost.…

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Q: Evaluate the following 1. S sin x sin (cos x) dx

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Q: \1/2 2. y = (2 tan² 20-1)

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Q: Find a critical point tid b.) relative maximum value valve C.) Relative mini mom d.) inflection…

A: Note :-  Here Equation of g(x) = 2x2-9x2+27 =-7x2+27 Or g(x) =2x3 -9x2+27  So we solve this problem…

Q: Let ₁1 and In+1 = limit. 1 for n N. Show that this sequence is convergent and find its In + 2

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Q: Consider the following. y = 4x³ - 3x2 Find the relative maxima, relative minima, and points of…

A: Given problem:- f(x) =4x3-3x2  To find:- Relative maximum Relative minimum Inflection point Graph…

Q: (b) D₂f = 2 cos(xy + 2z) Dzzf = -4 sin(xy + 2z) Dzzyf = -4x cos(xy + 2z)

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Q: Evaluate the definite integral. NOTE: Enter the exact answer. | ||ti + 1²3|| dt =

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Q: Determine the angle between the two lines: 1₁: 7 = (1,0) + t(0, —2), t ¤ R x+2 y-3 and 1₂: *+² = −³.…

A: Given

Q: Use the One-to-One Property to solve the equation for x. - 2x 7 = 4 X =

A: we have to slove the above question and find the value of x

Q: X 1.-+ J y = 37ab2, y" X

A: Let's find.

Q: y = 1- cos 0 1+ cos 0 3

A: Solution of given question is written in below steps.

Q: Evaluate the following x4 (5-x²) dx

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Q: A. Write the expression as a single Integral. Choose your answer from the box. Letters only. A. f…

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Q: Evaluate the following integrals. Show complete solution and your answer must be in simplified form.…

A: To Find :   ∫11+cosxdx

Q: Find the laplace transform of f(t) = 2t¹-3e³t+10 cos 2t

A: Given that,  f(t)=2t4-3e3t+10 cos2t

Q: 2) √ x¹ (5-x²) dx

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Q: Find the arc length L of the graph of r(t). r(t) t L= = ³²³i + 1 j + 1/2 √√61² k, 25157 = i

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Q: Find the derivatives of the following function (a) y=4²+2 2x+3 2³+2+1

A: The solution is as follows:

Q: Write an equation of the form y = a sin bx or y= a cos bx to describe the graph below. Ty 0 1 nin 1…

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Q: Income flows continuously into a manufacturing company at the rate of 36, 450e 0.052t dollars per…

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Q: 1. find dy/dx of each equation using implicit differentiation. a. x2 - y2 = 9 b. 3x2 - y3 -3xy = 0

A: As we know that; The Power law; ddxxn=nxn-1 The Product rule; f·g'=f'·g+f·g'   Given: (a). x2-y2=9

Q: Evaluate the integral. JS 2x + y dA D where D is the region bounded by y=x, y=0, x=2.

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Q: #6

A: Topic:- application of integration

Q: 2x²+x-1 Evaluate -dx using method of partial fractions. Which of the (x-1) (x³+1) following is the…

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Q: g(t) How many people contracted the lu 7. Suppose that f(t) is the rate at which snow is falling at…

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Q: Question 5 Find the derivative [f(x)]; f (x) = 3 ln (In (x²-3x + 5)²). O3(2x-3) ²-3x+5 3(2x-3)…

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Q: Determine whether the improper integral diverges or converges. 00 √x³²e-x dx O diverges Evaluate the…

A: To find the integral: ∫0∞x2e-xdx converges or diverges.

Q: 6. Determine the x-value of the absolute minimum of f(x) = -2x4 + 4x³ - 1 on the closed interval…

A: Given:       fx=-2x4+4x3-1     f'x=ddx-2x4+4x3-1    f'x=-8x3+12x2

Q: Evaluate the iterated integral. 6 (x + y) dy dx Jo Jo

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Q: B. Find the first and second derivatives of the following: 1. m(x) = 2(x)(√x) 2. a(x) = √3x 3. [u(x)…

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Q: 1. Given the following matrices: A = 1 2 3 4] 24 6 8 1 3 5 7 -1 2 -3 4 a. [(AC)BT] - DT b. [(BD)…

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Q: Comput: f dx 2+x

A: I am attaching image so that you understand each and every step.

Q: The equation below gives parametric equations and parameter intervals for the motion of a particle…

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Q: дz State the multi-variable chain rule for du z=z(t, s), t=t(u, v, w), s=s(u, v, w) if

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Q: Evaluate the following integrals. 2. √x* +5x³+ x+5x³+20x+16 x(x²+4)² dx

A: Solving

Q: Evaluate the following: 1) S x² √1 + x dx

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Q: A Cessna plane takes off from an airport at sea level and its altitude (in feet) at time t (in…

A: Given: ht=2000lnt+1 Rate of climb will be rate of change of height i.e. dhdt

Q: INSTRUCTION: Prove or disprove 1. 3x-5 = is bijective. 2x+1 Show that f: R-{-}→R-{} defined by f(x):

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Q: Je-2x sin 2x dx

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Q: Evaluate the iterated integral. 8 3 (x + y²) dx dy -1/1

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Q: The cos³dy is {A}-sin+sin³+C 3 3 3 4 {B} sin¹-sin³+ C 3 4 3 4y (C)-sin-sin³+C {D}sin+sin³+ C

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Q: Find d² y dx² for x³ + y³ = 2 43

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Q: 21 te 1 1 1-2 1-2 None of the alternatives are correct If L <=lim In p-400 then f(t) is 0+2

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Q: Find Lt+1)²-e' sin² t + cos(t+1 ++ π)}.

A: Given :