Find the unit tangent vector T, the principal unit normal vector N, and the unit binormal vector B for the helix r(t) = (cost, sint, t).

Q: 1. (a) First find the following indefinite integral A. e666 B. 2e667 (e - 1) e√x+666 [= √x dx = (b)…

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Q: Consider the following double integral 1 = ₂ x dy dx. By converting / into an equivalent double…

A: Given :- I=∫-33∫-9-x20dydx convert given integral to polar conversion

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A: The objective is to find s(h).

Q: (1) f (1) x²(x³ +1)5 (x³ − 1)5 dx -

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Q: (1) f(x+4)² dx (3) ſ. x² dx x² - 4 (2) √ x²(x³ + 1)² dx (4) √x²0 x² cos 3x dx

A: The given integrals are;  1) (x+4)2 2)x2(x3+7)7 3)x2/(x2-4). Repost the 4th question.

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Q: 8) Evaluate the following without the use of a calculator arccsc(-√2)

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Q: 6. If y is a differentiable function of r and 24 + 2y5³ 5y2, then find - dy da

A: The given equation is x4+2y5x3=5y2

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Q: Determine the point(s) (if any) at which the graph of the function has a horizontal tangent line.…

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Q: It is a fact that the function  f(x) =  (9x2 − 2) (4x2 + 4)  has a limiting value. Use a table of…

A: We need to find limiting value.

Q: Find the exact sum of the following series O. In 3 2 1 In(3) --- / 2 In ( ²2 ) 32 3 In (²2) - ○…

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Q: Using the Limit Comparison Test with the geometric series -17, to 8 67 determine if the series given…

A: Limit comparison test -  If we have two series ∑n=1∞an and ∑n=1∞ bn and limn→∞(an/bn) is finite and…

Q: Find an equation of a line that is tangent to the graph off and parallel to the given line. Function…

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Q: (D²+4D+5)y=35e : y(0)--3, y'(0)-1

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Q: Use Stokes's Theorem to evaluate F. dr. Use a computer algebra system to verify your results. In…

A: Here,  g(x,y)=49-x2G(x,y,z)=z-g(x,y)

Q: Find the value of the derivative (If it exists) at the Indicated extremum. (If an answer does not…

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Q: 4. Let g(x) = f(t)dt, where f is the function whose graph is shown. (a) At what values of a do the…

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Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A: I have stated the used formula in the solution

Q: Solve: y(1) Given: y'-y=1, y(0)=0

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Q: Consider the following. (Round your answers to four decimal places.) f(x, y) = x cos(y) (a) Find…

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Q: 3 A merry-go-round has a radius of 4 m and is spinning at a rate of 0.5π radians/s. Bill is standing…

A: Formula used: Circumference of circle = 2π×radius of circle  velocity =  angular velocity × radius

Q: Find the absolute extrema of the function (if any exist) on each interval. (If an answer does not…

A: Topic - Extremas of the function

Q: = If cot(x) Give exact answers. sin (²) cos (77) tan(72) = 18 5 = Submit Question (in Quadrant 2),…

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

Q: Use synthetic division to find the result when 3x4 - 3x³ +16x²-117-31 is divided by a + 4. Write…

A: answer is in next step . please give a like !!

Q: 15. 1/√/2 X 1+ 4x4 dx

A: We need to evaluate :

Q: 4 cos x -dx 1+ cos x

A: Our Aim is to evaluate the integral given below:-∫cos4 (x)1+cos (x) dx -(i)

Q: Evaluate the integral using the following values. 8 ["x³ dx = 960, ["x dx = 24, ["dx-4 = J4 8 [²- x…

A: Gievn , Hint: 4∫8xdx=24   .....(1)

Q: Verify the Divergence Theorem by evaluating F.NO N ds as a surface integral and as a triple…

A: To verify the divergence theorem. And to evaluate the surface integral.

Q: (a) AB X AC (b) the volume of the parallelepiped determined by AB, AC and AD

A: As we know the expression for the volume of the parallelepiped is: Vp=AD→·AB→×AC→   The given…

Q: The graph of the polynomial f(x) is given below. If f(x) has degree 4, find the factored equation…

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Q: LORAN (long distance radio navigation) for aircraft and ships uses synchronized pulses transmitted…

A: answer is in next step , i can only answer one question as per guidelines.

Q: Identify the rational function whose graph is given below. Note the x-intercept of the graph is a y…

A: topic:- function

Q: Evaluate the indefinite integral: [ 10 10e¹x cos(2x) dx

A: We will use simple Integration rules to solve this question.

Q: t is a fact that the function  f(x) = x(161/x − 1) has a limiting value. Use a table of values to…

A: We need to find limiting value.

Q: (a) AB-BC (b) projABAC (the vector projection of AC onto AB) (c) the area of AABC

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Q: The graph of f is shown. y -10 0 10 y = f(x) 20 30 40 X

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Q: Where is f' = 0 ? at a What are the values in the closed interval [-1.2, 1.5] where f' undefined? at…

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Q: 16 Find the constants a,b,c for the conic r=- 5-3 cose Sketch the conic.

A: Given: r=165-3cosθ

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Q: Situation: An online retail company tracked total number of purchases monthly. In February 2007 they…

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Q: an I ask how the maximum and mininmum points were obtained?

A: We need to find max and min points.

Q: Does the series n=1 n5/4 converge or diverge?

A: The given series is 1/n5/4, n from 1 to infinity.

Q: Consider the function f(x) = 2x³ - 6x² - 18x + 54. a. Find the first derivative. f'(x) = b. List any…

A: As per our guidelines we only solve three sub parts of given question and rest of the sub parts of…

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = 2t² - 5 sin(4t)…

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Q: 5 1 So (125 + 25x + 6) dx 6o S X (1 + x²)3 dx / 1 + x² dx 1

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Q: 248 217 186- 155 124- 93 62- 31

A: topic:- calculus

Q: 2. π 2 cot x d

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