Find the length of the arc of the curve having the parametric equations x = from t = 0 to t = 1. t and y = 2t2 %3D

Q: bx a a dy dx 0.

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Q: sin2x de Evaluate:

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Q: Find the area of the region bounded by y = -x2- 6x- 3, y =-x2 -8x-13, x -5, x -2.

A: You need to understand which curve is upper and which one is lower. Then use the formula to calculat...

Q: Solve the problem. A company knows that the unit cost C and the unit revenue R from the production a...

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Q: Evaluate the integral. 16 In(y) dy Vy

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Q: The derivative of the function y = sin-1(e* – In x), where Je – In x| < 1, is:

A: Recall ddx(sin-1(x))=11-x2 ddx(ex)=ex ddx(ln(x))=1x

Q: Evaluate the integral. (Use C for the constant of integration.) | 2 csc*(x) cot (x) dx

A: We will use simple Integration formulae to solve this Integral.

Q: Find the volume generated by revolving the area bounded by y² – 4y – 4x + 4 = 0 and x 1 %3| about th...

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Q: a) Determine the cosine of the angles of the triangle whose vertices are A(1, –-2, 1), B(3, 0, 2), C...

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Q: Suppose the rate at which consumers purchase peanut butter is increasing at a rate given by  f ′(t) ...

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Q: Evaluate: sin® (÷ cos? 2. (() dx

A: We we will find the value of the integral. 

Q: Use the formula for the binomial series: m(m–1) ,2 + (1 + x)" = 1+ mx + 2! m(m–1)..-(m-k+1), k! %3D ...

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Q: The values of C, and C, so that y(x) = C, e3x + C, e-3x satisfies the %3D following conditions: y(0)...

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Q: Find the values of a and b if the tangent to y = ax² + bx at (1,5) has a slope of 8.

A: We can find the value of a and b as below

Q: The derivative of the function y = log2(In(x)) is: 1 1 y': x In 2 In x y' = x In 3 ln x the above th...

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Q: Which of the following best describes the function below? (3x ifxs2 x if 2<x f (x) =

A: Checking limits:When x approaches to 2 from left side:=limx→2- f(x)=limx→2- 3x2=3(2)2 =12When x app...

Q: Find the volume of the solid obtained by rotating the region bounded by y = x , y = 0, a about the y...

A: Given query is to find the volume finthe solid generated.

Q: Select ALL possible answers if there is more than one. (3-2x ifx<2 [3x-7 if 2sx' Which of the follow...

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Q: spac characters. * d Compute de y -8 at r =2. y +8

A: Topic:-  derivatives

Q: Show your work to justify your answers. Write your solutions properly, neatly, and carefully. s) Fin...

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Q: Tim Hortons estimates it will have a continuous income flow of  f (t)  =  4311 dollars per year from...

A: Given income flow f(t)=4411 dollar.

Q: Find the centroid (, j) of the region bounded by: . y = 3x + 8x, y = 0, x = 0, and x = 6 %3D y =

A: The given problem is solved below in detail.

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

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Q: bx a a dy dx

A: Our Aim is to evaluate the integral given below:-∫0a∫0bxady dx -(i)

Q: Question 3 Determine whether the improper integral converges or diverges. 14e5x dx A Diverges B Conv...

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Q: dy using implicit differentiation, for the equation a + y 7 is. Find da

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Q: Evaluate: " sin7 cos4 dx

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Q: Find the relative extreme of the function f (x) 12+2x+2 and where they occur.

A: Given: - The function is, f(x)=x+1x2+2x+2 To find: - The relative extreme of the given function.

Q: 1. lim(2x + 4) x-3

A: "Since you have asked multiple questions. We will solve the first question for you. If you want any ...

Q: d) f(x) = e) р(х) %3D (е* + 1)(е* — 1) x3

A: Given: To find derivative of  d) f(x)=exx3 e) p(x)=(ex+1)(ex-1)

Q: Determine whether the series converges using the Ratio test. 00 7k k=1 The series

A: This question is based on Ratio test.

Q: Write an equivalent double integral with the order of integration reversed. dy dx dx dy dx dy ©SS ax...

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Q: nd the area of the region bounded by y = –x² – 4x – 2 and y = 2x² + 8x + 7.

A: To find out the area of the region bounded by the curves. 

Q: Find F' (÷) if F(x) = 2 cos-1 Vx. %3D

A: We will find the value of F'12 where Fx=2 cos-1x in the following step.

Q: Do not round any intermediate computations. Round your answers to the nearest degree. 1. Let v =-7i+...

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Q: f (x, y) = xª – 2.x² + y² – 4y + 5. a) Use the second derivative test to find the critical points b)...

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Q: Find the arclength of y = 2x/2 3/2 on 1 < x < 3

A: We know that the arclength of a curve y=f(x) on a≤x≤b is given by L = ∫ab1+f'(x)2 dx

Q: Find an equation in the form y = ax² + bx + c_whose graph has an x-intercept at x = -1 and a tangent...

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Q: 90 cos(0) d0; u = 90, dv = cos(0) de %3D

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Q: - 20 - dr x² Vx? + 64 Evaluate the integral:

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Q: 3. The Cartesian coordinates of a point are given. (i) Find polar coordinates (r,0) of the point, wh...

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Q: 5. Determine the slope of the tangent at point (1,5) on the graph of f(x) = (9 – x²)} + 1.

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Q: 4 Vva – 1dx 2

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Q: aracters. * mine the slope of the tangent line to the graph of f(x)=-- at the point (4,-4).

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Q: Question 6 Evaluate the double integral over the given region. S *+x4 - 3) dA, R: 0 sx s1,0 sy s2 15...

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Q: - The appropriate integrating factor for the following differential equation (2x + cosy)dx + (x²tany...

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Q: Using an appropriate substitution, 3 the integral S dx equals: V1-4(x-1)2 3 sin-1(2x – 2) + C sin-1(...

A: We can find the integration as below using proper substitution.

Q: The integral of t2ln t with respect to t is; 13 A -(In t- 3) +C B none of the given choices -(3In t ...

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Q: 14 If f(x) : t? dt then f'(x) =

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Q: From the following results, determine whether the function 2x +9, r 9 f(x) = 6. is continuous at = ...

A: Solve for the continuity for the function