. Find the arc length of the cycloid defined by the parametric equations x = 0 -sin and y = 1- cos between 0 = 0 and 0 = 2TT.

Q: h (x) = x² lnx, at

A: Topic:- function and it's derivative

Q: The graph of a derivative f' is shown to the right. Use the information in the graph to determine…

A: To find the intervals where function is increasing or decreasing.

Q: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to…

A: Given    4 intervals

Q: 3 3x-1 f(x) = 4x²³²³-x + ³x-

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Q: A cylindrical can, open at the top, is to hold 200 cm³ of liquid. Find the height, h, and the…

A: given volume is v=200 cm3

Q: lim ln x x-0

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Q: Find the angle between the vectors (6, 30√3) and (30√√3, 12). (Express numbers in exact form. Use…

A: let a→=6,303 and  b→=303,12

Q: ㅍ (2) Evaluate (cos(3x) — sin(x))dx. - 6

A:

Q: Use transformations of the absolute value​ function, f(x)=|x| to graph the function g(x)=−x−2+7.…

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Q: 2) g(x) =x2+3x-5, afx = 1

A: We need to find out the derivative of the given function at x=1

Q: What is/are the x-value(s) of the relative minimum/minima? Select the correct choice below and, if…

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Q: 0 -5 3) a) Given four points on the function y = f(x), A(-3,0), B(0,6), C(2,-2), and D(3,0), find…

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Q: elnx 8) fex dx g) √1-e²t dt (Hint: let u = e¹) h) fx dx dx (let u = x¹/2)

A: g)∫elnxxdx

Q: ellipse at (2, 1)_

A: a. point ( 2 , 1 ) x = 2 , y = 1 Therefore point is on ellipse

Q: Find particular solution of the differential equation in the attached  image

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Q: Evaluate the integrals for f(x) shown in the figure below. The two parts of the graph are…

A: Note to student : Hello. The submitted question has 4 different parts. As per Bartleby answering…

Q: Find the local maximum of the function f(z), which is given in the graph below. Give your answer as…

A: Topic- Local maximum of a function We are given graph of a function. Local maximum on the graph is…

Q: x³-1 lim x+1√√x-1

A: The limit is given by limx→1x3-1x-1 To evaluate: The value of the limit using table.

Q: Write the first trigonometric function in terms of the second for ? in the given quadrant. sec(?),…

A: Topic : Trigonometry

Q: 55.0 g +9.76 dg + 5.67 mg = ?g

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Q: 15. f(t) = 1 + cosh 5t

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Q: [² Find X dx. Hint: Choose a to be the geometric mean of xi-1 and x; (that is, x = Value of integral…

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Q: For this discussion post, I will ask you to sketch some graphs that meet a limit condition and…

A: To be found - Sketch of different functions with given conditions. Topic - Function, limits &…

Q: Question 6. Find an equation for the surface consisting of all points P that are equidistant from…

A: See this solution in below.

Q: Consider the partial derivatives Is there a function f which has these partial derivatives? Yes Ⓒ If…

A: We need to write down that is there any function having the given partial derivatives.

Q: 3x²+2x²+x iii) fi dx

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

Q: Find the equation of the line tangent to the graph of f(x) = (In x)4 at x = 2.

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Q: Find f', given f'(x) f(x) = * sin(x4) x² +1

A: To find derivative of the function.

Q: A particular curve passes through (1, 1) and satisfies the differ- ential equation dx = (1-3y²³) dy.…

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Q: 1. Find the solution of the given initial value problem. y" + 2y + 2y = 0, y(π) = −1, y'(π) = 0.…

A: Given, the differential equation is Y''+2Y'+2y=0 Now, the differential equation can be rewritten…

Q: If f and g are the functions whose graphs are shown, let u(x) = f(g(x)), v(x) = g(f(x)), and w(x) =…

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Q: QUESTION 9 Evaluate x sinx dx O xeosx = sinx +C O-xcosx - sinx +C O xcosx + sinx + C O-xcosx + sinx…

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Q: 1 dx/(x² + x√x)

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Q: oblem 8. (a) [e² sin (r) (b) [ (x+3) ln (x) (c) [²* (In (2))² da dx Calculate each of the following…

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Q: 1. The rate of cooling of a body is given by, dᎾ = k0 where k is a constant and I is in ºc dt Find…

A:

Q: 5. Compute and simplify the difference quotient f(x) = 3x² + 7x-2 f(x+h)-f(x) h 9 h = 0.

A: We have to slove above questions

Q: If m ≤ f(x) ≤ M for a ≤ x ≤ b, where m is the absolute minimum and M is the absolute maximum of f on…

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Q: Find: i) fx³dx ii) f8y³ dy

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Q: 4x + 1 4x² + 1 Find f'(x), and then evaluate ƒ' at x = 2. f(x) =

A: f(x)=4x+14x2+1

Q: Evaluate OI 4 sin ³x dx sin*x + C -sin¹x + C +cos³x + C -cost + +C cost --cos³x + C

A:

Q: дz дz Let z = sinh(7x + 8y). Find and ax ду дz ax дz ду || 7 cos(7x + 8y) 8 cos(7x + 8y) х х

A:

Q: Find the equation for the tangent plane to the surface at the indicated point. (Hint: Solve for z in…

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

Q: Use Euler's method with step size 0.5 to compute the approximate y-values y1, 32, and y3 of the…

A:

Q: n regards to expressing revenue R as a function of p:  R(p)= -6p2+ 180p What is the revenue if the…

A: we can find Revenue .

Q: Determine the curvature of the elliptic helix r = : (7 cos (t), 8 sin (t), 8t) at the point when t =…

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Q: Sketch the graph of an example of a function f that satisfies all the given conditions. lim-of(x) =…

A:

Q: - · r(t) = (3t — t³, 3t², 3t+t³)

A: From the provided curve, rt, to determine the arc length from t=0 to t=b.rt=3t-t3, 3t2, 3t+t3

Q: Determine f-¹(x). ƒ¯¹(x) = = -x² + 16x What is the domain of ƒ-¹(x)? What is the range of ƒ−¹(x)?||…

A: P

Q: Use an appropriate substitution to solve the differential equation ² ( ² ) ) dx - + cos² - X dx - x…

A: we need to find out the solution.

Q: The graph of a derivative f' is shown to the right. Use the information in the graph to determine…

A: Given that the graph of a derivative f' is shown to the right.