Use the formula r(t) = |r(t) × r"(t)|l| ||r(t)||³ to find k(t). %3D r(t) = t’i + t3j K(t)

Q: What isfor the curve given by x = (t – 1)³ and y = vt ? | dx 1 2VE 6VE(t-1)2 3(t-1)2 O Option 4…

A: Using chain rule of differentiation

Q: What is the domain of y =f"(x) if f(x)=;(x-1)*?

A:

Q: Find the point where the tangent line to y = 5x at x = 0.5 crosses the x-axis.

A:

Q: x+3 Where is f(x) discontinuous? 2²+4x+3 О-3,—1 O -1 O -3 O f (x) is continuous everywhere

A: To determine the points where the given function is discontinuous.

Q: A famous leaning tower was originally 184.5 feet high. At a distance of 130 feet from the base of…

A: Using sine rule, all parameters are evaluated.

Q: (3t – 1)66 dt

A:

Q: If f(x) = | ( + 2t² + 2)dt then = (x),,f

A: f(x)=∫0xt3+2t2+2dt

Q: what is the exact answer

A: The exact answer was the second last line of the original solution.  So, the exact answer is:…

Q: To evaluate the Integrals, use the additive Interval property of Integrals which Is glven as…

A: answer is in next step

Q: your

A: Please refer to the image below

Q: c). Using an integrating factor solve the equation dy + 2y/x = x dx

A:

Q: The point is on the terminal side of an angle in standard position. Find the exact values of the six…

A: Given that the point is on the terminal side of an angle in standard position. To find the exact…

Q: Evaluate the following algebraically. csc? x lim 1 O 1 O -1 8. 8.

A:

Q: 9. S (6eº+1)/½ eo 10. |(1 + 2x)³ dx

A: We can solve as follows

Q: If fex) x2 f'co) 19+ t? dt find f'c3) %3D

A:

Q: For x = t3 + 2, y = 3 – t, give an equation in terms of x and y.

A:

Q: Show that the function f defined by 1, (x, y) = (1, – 1) f (x, y) : .2 x + y (x, y) # (1, – 1) x + y…

A:

Q: Find the exact value of the expression, if possible. (If not possible, enter IMPOSSIBLE.) cor…

A:

Q: dx Half-angle Substitution cos x +sin x-1

A:

Q: Use the properties of logarithms to expand the expression as a sum, difference, and/or constant…

A:

Q: Find the distance from A to C across the gorge illustrated in the figure. 130 ft The distance from A…

A:

Q: Determine the general solutions of the following differential equations. 1. (2x - xy2 - 2y + 3)dx –…

A: We can solve 1 problem only.

Q: 10) Eind the eçuation of the plane Contaihins the two vectors 2and ,and the point PU2ー)

A:

Q: Find the Indefinite Integral and check your result by differentiation. (Use C for the constant of…

A:

Q: Q2) Find the integral of: 6 tan*x dx

A:

Q: 3. Use chain rule to find given w = Vx2 +2y2 + z² and a cos (st), y = -2s In t ane 2 = 3s?Vt. 3s2Vt.

A: Follow the procedure given below.

Q: xdx 41. 12-х

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

Q: 2t +1 lt +8 -dt + 4t +4t 3

A: Let's find.

Q: for the N(0) is it 0k? or can I write it just k?

A: Yes, N0=-12i+12j+0k.

Q: Evaluate csc2 3z dr cot 3r O 6cot 3xcsc3x + c O cot 3x + c Ocot 23xcsc3a + c cot 23x +c

A: Indefinite integration

Q: anUNIVE Q3) Find the integration: - (x+1)vx2+2x

A: As you have asked multiple questions so I have answered only first question as per the…

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of 12 fe) = [, (; - )". dt…

A:

Q: 13 of 20 limz→-6 746 a+6 Does not exist 8.

A: Let's find.

Q: Find fr(x, y) and fy(x, y) given f(, y) = (csc y) Arcsin(x²). %3D

A:

Q: Find the limit of s(n) as n . 1 n(n + 1) s(n) = 5.

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Q: Select the best answer. (2e + 1)= lim (tan(x))- O DNE O -00

A: We have to find out limit

Q: 5. What is the general solution of the following differential ,d*y 6. equation 'dx+ d³y.od?y dx2 dx3

A:

Q: Find F as a function of x and evaluate It at x = 0, x = 7/6, and x = 1/2. F(x) = sin 0 de %3D F(x) =…

A: We have to find out the integral

Q: chain rule to find given w = x² + 2y² + z² and x = cos (st), y = -2s lnt an 3s2 Vt.

A: We have to find out derivative

Q: dg 1+sin 2x Find of g(x) dx 2x-tan 2x

A: To find the derivative of given function.

Q: A cylinder (round can) has a circular base and a circular top with vertical sides in between. Let rr…

A: Given ,  A cylinder (round can) has a circular base and a circular top with vertical sides in…

Q: Evaluate the Integral using the following values. 8. * dx = 1,020, x dx = 30, dx = 6 (7x 11x +4) dx…

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Q: Step

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Q: (-5 S + (0.9)" | lim

A: Given query is to find the value of the indicated expression.

Q: D. Find the orthogonal trajectory f the family of curves y= x+h %3D

A:

Q: х — у 3. f(x, y, z) = y? + z? а. f(3, –1, 2) b. с. d. f(2, 2, 100)

A:

Q: Q2) Find the integral of: L*„6 tan*x dx 4

A: LetI=∫-π4π46tan4xdxTake the constant…

Q: Match each point in polar coordinates with either A, B, C, or D on the graph. D

A:

Q: If f(-x)=(2,-1), what are the coordinates of f^(x)?

A: Given that,  f-x=2,-1

Q: Solve using product rule d(uv) = u dv + v du: f(x) = (3x^2 – x + 4) (2x^2 – 1)

A: Our Aim is to solve the given function using the Product Rule where f(x)=(3x2-x+4)(2x2-1)