Consider the following vector function. r(t) = (4 sin(t), t, 4 cos(t)) (a) Find the unit tangent and unit normal vectors T(t) and N(t). T(t) E N(t) PM

Q: Find the volume of the solid obtained by rotating the region x², y = 0, and x = 1, about the y-axis.…

A: NOTE: Refresh your page if you can't see any equations. . here we have ..............radius…

Q: 1 Given that sin A = and tan B = 1, and that angles A and B are both in Quadrant I, find the exact…

A: sinA=126 and tanB=1 ,A and B in Quadrant I

Q: Evaluate the definite integral. [° ( Z - ²3/) dx J₁ X

A: ∫16x6-9xdx

Q: Find the differential of the function. z = x ln(y5 + 2) dz = )dx + ( Jay dy

A: Finding a function's derivative is a step in the mathematical process known as differentiation. The…

Q: Recall the Chain Rule and how it can be applied to find the derivative of a composite function. In…

A: For each of the following functions, by using chain rule to find the  function's derivative. (i)…

Q: The initial and terminal points of AB are given below. Write the vector in component form. A (-5, 2)…

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Q: Find the volume of the solid formed by rotating the region enclosed by y=e¹ +3, y=0, x=0, x=0.8…

A: Consider the given function y=ex+3, y=0, x=0, x=0.8The volume about x axis is evaluated  as…

Q: Determine x = f(t) for dx (t² + 6t). dt = 6x + 6, t> 0; f(1) = 9.

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Q: 1. 2. Find f'(x) and f"(x). Determine the following Domain a. b. x and y intercepts t. The critical…

A: derivative calculated by differentiation with respect to x

Q: Function f(x) is positive when 1<x<2, and it is negative when 2<x<3. If the area of the region…

A: If Function fx is positive in a,b∫abfxdx=Area under the curve fx over inteval a,bIf Function fx is…

Q: A bucket begins holding 30 kgs of sand. The bucket is to be lifted to the top of a 20 meter tall…

A: We have the formula, F=ma In our case, m= (30-0.3x) a=9.8 Therefore, F=(30-0.3x)9.8 =294-2.94x

Q: (d) 2 fra -2 f(x) dx =

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Q: ) Based on your experience in parts (a) and (b), conjecture an antiderivative for each of the…

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Q: 3) Find the area bounded by the parabola x = 9-(y-2)² and the y-axis.

A: We know that area formula int_a^b f(x) dx

Q: 25. an = ln 12n+2 −9+4n

A: Given :an=ln12n+2-9+4n

Q: Consider the integral 9 3 1² ( 2²/2 + 5) dz dx X (a) Find the Riemann sum for this integral using…

A: Given integral  ∫59( 3x + 5 )dx

Q: 5) Calculate the Taylor polynomials T₂ (x) and T3 (x) centered at x = a of the function f(x) = sin x…

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Q: (a) The series For the following answer blanks, decide whether the given sequence or series is…

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Q: Use Newton's method with the specified initial approximation x, to find x3, the third approximation…

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Q: Find the maximum rate of change of the function f(x, y) = DNE 2y² x at the point (2,4)

A: The function is given by fx, y = 2y2x The point is 2, 4 To evaluate: The maximum rate of change of…

Q: f(3)= 7 and f'(3) = -3 find d/dx sin^2 (f(x)) at x = 3

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Q: дz əz Use the chain rule to find and Əs at z = (x - y)², x = s²t, y = st² əz as əz at || =

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Q: Use the integral test to determine whether each of the following series converges or diverges. For…

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Q: 61. an = nsin RIS n

A: We find the limit of given sequence.

Q: Find the derivative of f(x)=; in final answer -2x 13/4x² +11x with no negative exponents

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Q: The following table gives values of a continuous function. X ave 20 25 30 f(x) 41 38 29 35 40 45 50…

A: The following table gives values of a continuous function. x 20 25 30 40 45 50 fx 41 38 29 26…

Q: Maximum and minimum value 2) at Find the critical numbers F(x) = x ³ (4-X) OF bi Find the absolute…

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Q: 65. an (1 + 1/1) n

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Q: Q1: Solve the following equations system, using Gauss elimination method 4y1 + 2y2 +3y3-5 =6 3y₁ +…

A: We need to solve the given system of equations using the gauss elemination method which uses the row…

Q: Suppose that we don't have a formula for g(x) but we know that g(2) = -4 and g'(x)=√√x² + 5 for all…

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Q: The top and bottom margins of a poster are each 9 cm and the side margins are each 6 cm. If the area…

A: The top and bottom margins of a poster are each 9 cm and the side margins are  each 6 cm. If the…

Q: Find the second partial derivatives of the function f(x, y) = x³y5 + 2x5y. a2f дх2 1. 2. 3. 4. - 82f…

A: The function is given by fx, y = x6y5+2x5y To determine: The expression of the following second…

Q: Marginal Cost A division of Ditton Industries manufactures a deluxe toaster oven. Management has…

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Q: Find a quadratic equation with the given roots. Write your answers in the form Ax2 + Bx + C = 0.…

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Q: How did you get from (x2+8x+15) to (x+3x+5)? How did you get from (x+3x+5) to (x+3)(x+5) for the…

A: Given Limit  limx→-3sinx+3x2+8x+15

Q: The process of synthetic division applies equally well when some or all of the coefficients are…

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Q: Evaluate the integral. म (3ex+ 5 sin(x)) dx

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Q: 57. Yn = en 27

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Q: Find the component form of vector with initial point (-6, 2) and terminal point (7, -3). O v = (-8,…

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Q: y = x³, y = 0, x = 2 . Find the volume created by revolving about a = = 3. Use washer or disk…

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Q: Find area of the region under the curve y = 4x³ - 2 and above the z-axis, for 3 < x < 8. area =

A: We know that the area of the function f(x) at x=a to b is  int_a^b f(x) dx

Q: Use the standard Maclaurin series for sin(x) and cos(x) to find the first three non-zero terms in…

A: We have, Maclaurim series for sin x and cos x

Q: Use differentials to estimate the amount of metal (in cm³) in a closed cylindrical can that is 26 cm…

A: Volume of the cylinder = πr2h where r is the radius and h is the height of the cylinder.

Q: Create a limit evaluation problem that requires substitution with an answer of 1.

A: limit evaluation problem

Q: (b) lim (4x) = 818 8 (c) lim -6x= 8118 (d) lim -6x = 818

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: 25. Practice similar Help me with this Use the ratio test to determine whether an+1 lim n→∞ an (a)…

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Q: 8) A particle that moves along a linear path has a known velocity of v(t) = 4.3 sin (2.1t), where…

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Q: Find the general antiderivative. Use c as the constant of integration. (6cos(x) - 2) dx

A: We know the antiderivative of cosx is: sinx+c Where, c be the constant of integration.

Q: Use the chain rule to find dw dt = dw dt w = In (√x² + y² + z²), x = 8 sin(t), y = 7 cos(t), z = 2…

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Q: where r(t) is 12) The growth rate for a 24-hour period of a bacteria colony is measured to be r(t) =…

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