Find the arc length L of the graph of r(t). r(t) = 12 cos(t)i+ 12 sin(t)j + tk, 0

Q: Evaluate the definite integral by interpreting it in terms of areas. 8 (4x - 24)dx stion

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Q: You decide to create the digits of a decimal number y between 0 and 1 using the function f(n) = 3n +…

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Q: Question 5 Given that f f(x) dx = 3 and f f(x) dx = 4. A) S₂ f(x) dx = B) f²3f(x) dx C) f f(x) dx =…

A: topic - definite integral

Q: 8. Find the derivative of the function f(x) = x ² - 10x + 3 using First Principles.

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Q: A function is said to have a horizontal asymptote if either the limit at infinity exists of the…

A: limx→∞ x2+8x3-11x=limx→∞ 1xx2+8x1x(3-11x)=limx→∞ x2+8xx23x-11

Q: b) c) dx x²(x²-16)2 S S- dx 1 (4x²+3)2 S. X = X = dx = dx =

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Q: The gradient of f(x, y, z) = xy²z³ at the point (1, 2, 1) is

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Q: Find the limit. If you L'Hopitals Rule, make sure to justify why you can use i use lim 2?e

A: We have to find the limit.

Q: 58. 10 (k² - 4k+7)

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Q: Q1) Use explicit finite difference method to solve the following differential equati

A: answer is in next step

Q: 2. If the Profit function for producing x units is P(x) = 0.0035x³ + 120x, then the marginal profit…

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Q: 3. Find an equation of the tangent plane at P = (0, 3, –1) to the surface with equation ze" + elz+1)…

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Q: Write the following expression as a single definite integral of the form [²f(x) dx + [²³1(x) dx - [~…

A: Given query is to find the value of the integral.

Q: Suppose that f(1, 0, − 1) = 2, and f(x, y, z) is differen- tiable at (1, 0, -1) with Vf (1, 0, -1) =…

A: We have to find out equation of tangent plane and parametric equations of normal at point (1,0,-1)…

Q: Simplify the following expression. X d * J V4+t* dt (Hint: Vi+Pt ,2 1 +t dt = + dt + dx - X -X -X

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Q: Evaluate the function at the indicated value of x. Round the result to three decimal places.…

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Q: full

A: We will find the double derivative.

Q: D(x) = 62-0.1x

A: answer is in next step

Q: Plot the curve r = 1+sin 8. Then find the length of the curve.

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Q: Find the k-component of (curl F) for the following vector field on the plane F=(x+y)i + (8xy)j

A: Solution: F=(x+y)i + (8xy)j       P             Q k-component

Q: 9) Evaluate the following indefinite integrals a. [(5x¹ + x² + x) dx b. 9x²(x³ +5)*dx c. S7 C. dx…

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

A: topic - application of derivatives and integrals

Q: 2. Given f(x)= x³ + ax² + bx has critical numbers at x = 1 and x = 3, find a and b.

A: Given query is to find the value of a and b.

Q: Write √x+y²+2x-y=3 +y²+2x−y=3 as a polar equation r = f(0).

A: Write in Polar equation

Q: Consider the double integral %3D (a+ 2)? + y = 4 Where R is the region of Xy given x² + y? = 4 find…

A: Given problem:-

Q: QUESTION 12 Find d²y/dx². x=1+1²y=t-³

A: Given;  x=1+t2, y=t-t3

Q: Evaluate the integral of the following using Miscellaneous Substitution dx 1+ X

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Q: Evaluate the integral of the following using Miscellaneous Substitution dx 4. Sa

A: We can evaluate the given integral by using the substitution u = x⅙  and the following formulas.

Q: A piece of wire is with a length of 4 m is cut into two pieces, and the resulting two pieces are…

A: According to given,    Let x be length of the portion that is bent into a circle   Therefore, 4-x=…

Q: B. Find the area of the region bounded by the following: 20. inside 1-² = 2 cos 20 and outside = 1

A: We need to find area of region.

Q: The equations for free fall at the surfaces of Saturn and Jupiter (s in meters, t in seconds) are s…

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Q: In Exercises 33-42, determine if the given vector field has a potential. If so, find one. 34.…

A: Solved below

Q: QUESTION 9 Eliminate the parameter to find a Cartesian equation of the curve. x = e²¹ - 1, y = 4f

A: Given that    x = e2t - 1  ,  y = e4t  We have to find the cartesian equation of the curve to…

Q: 4. x³ dx (x²+2)³

A: We have to calculate the given indefinite integral according to the given information

Q: You are taking a multiple choice test that has 10 questions. Each question has 7 answer choices with…

A: A multiple choice test that has 10 questions. Each question has 7 answer choices with one correct…

Q: Evaluate the limit 5 + 71 lim 2 - 5x

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Q: Use the table below to answer questions 8 and 9. x 1-3 4 f(x) -3 1 -2 f'(x) 5 -1 6 g(x) 4 7 -3 g'(x)…

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Q: Which of the following statements are TRUE? (Circle ALL that Apply) Optimization can mean…

A: Two multiple choices questions are given. These questions are from algebra and calculus. We have…

Q: A coal-burning electrical generating plant emits sulfur dioxide into the surrounding air. The…

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Q: 00 2 10) Evaluate the improper integral dx. Use limits as needed 8

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Q: Find the surface area of the region that comes from rotating the given curve about the y-axis: x =…

A: If x=x(t) and y=y(t) then surface area of the region rotating about y-axis is given by…

Q: QUESTION 11 Find an equation of the tangent line to the curve at the point corresponding to the…

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Q: 6. Find the intervals on [0,27) where f(0) = sin² (0) is concave upward/ concave downward.

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Q: - 3x³ - 5: For the function y = f(x) = df a. Find at z = 2. dx f'(2) = b. Find a formula for x = f…

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Q: Find the area of the region enclosed by the graphs of x = y³ - 14y and y + 3x = 0.

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Q: Exercise (2) - Solve using paper solution. d²y dy 2- - y + x = 0 dx² dx Solve using…

A: Find your answer below

Q: Evaluate fx cos x dx

A: Solution: