Express the limit as a definite integral on the given interval. lim n→∞ i = 1 exi 3 + X; Ax dx [0, 2]

Q: ying Polynomials Simplify the product using the distril (x-2)(x+6)

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Q: Estimate the average value of f(x) from x = a to x =b using the figure. The average value of f(x)…

A: We are given a graph of function . From graph it is clear that function is continuous on [a,b].We…

Q: a) x2+5x-14 x²+8x+7 + x²-4x+4 3x²-6x

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Q: For the following exercises, use the Mean Value Theorem and find all points 0 < c < 2 such that ƒ(2)…

A: The given function is,Take derivative.Substitute x=c

Q: The legs of an isosceles right triangle increase in length at a rate of 3 m/s.   Part A At what rate…

A: The legs of an isosceles right triangle increase in length at a rate of 3 m/s.Part A:To find the…

Q: ellipse: ² + ² = 1 4 Given the ellipse: (a) Find the coordinates of the center of the ellipse (a)…

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Q: Use the parametric equations of an ellipse, x = a cos(8), y = b sin(0), 0 ≤ 0 ≤ 2π, to find the area…

A: Given that the parametric equation

Q: If the marginal revenue for ski gloves is R'(x) = -0.5x + 55 and R(0) = 0, find the revenue…

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Q: Suppose parametric equations for the line segment between (4, 2) and (4, - 2) have the form: [ x(t)…

A: The line segment between the points (4, 2) and (4, -2) has parametric equations,It is also given…

Q: Derive the formula of a circle using horizontal strip

A: We need to derive the formula of the area of a circle by using horizontal strip

Q: -7 4 3+y 2 1 -6 -5 -4 -3 -2 -1 -1 -2 -5 1 2 4 X 5

A: To write the equation of the following graph.

Q: Find the average value of the function g(t) = 1 + t over the interval [0, 4].

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Q: The first three terms of an arithmetic progression are 2x, 5 and 6 – x.(i) What is the common…

A: The objective of the question is to find the common difference, the 9th term, and the sum of the…

Q: (a) The graph in the figure given below is made of line segments joined end to end. At which points…

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Q: Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is…

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Q: S(3x+1) (3x²+2x+1)³dx

A: I=∫(3x+1)(3x2+2x+1)3dxSubstitute 3x2+2x+1=u

Q: Perform the following operations and simplify the results. State the domain restriction in each…

A: The domain is the set of all possible input values  for a which function is defined.

Q: For what value of a is the following function continuous at every x? f(x) = x²-30, x<10 x≥ 10 ax,…

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Q: f(x) = f(t-sint) ³dt

A: f(x)=∫1x(t−sin⁡t)3dtProperty of definite integral∫abf(x)dx=−∫baf(x)dx

Q: 2 0 0 1 -2 1 0 4 -3

A: given matrix is ,

Q: lim У-у-г уг -30+2 зу Уже

A: We have to findlimx→−2

Q: Find the exact area of the surface obtained by rotating the given curve about the x-axis. x = a cos³…

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Q: Using rectangles whose height is given by the value of the function at the midpoint of the…

A: The given function in the interval .The aim is to find the area under the curve using the midpoint…

Q: A1. Milk or meat production Y per day is best explained by the inputs: feed needed per day in kg,…

A: The objective of this question is to determine the Lagrangian, find the First Order Conditions…

Q: logarithms. Express powers as factors. 1. A 50-mg sample of a radioactive substance decays to 34 mg…

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Q: y = In (14)

A: Given that expression we have to find the derivative of y with respect to t

Q: Use implicit differentiation to find the equation of the tangent line to the function defined…

A: The given equation is; 6x2+2x4y5=8Point (-1,1)

Q: Given that f (t) = t² - t - 5 represents the rate at which air is escaping from a balloon in liters…

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Q: Find the arclength of the curve x = 5t 9, y = 12t – 3 with 2 ≤ t ≤ 5. -

A: x=5t-9y=12t-3

Q: Sketch a graph of a function f with the following properties: the function is continuous on [-5, 5]…

A: Sketch a graph of a function f with the following properties:the function is continuous on [-5, 5]1.…

Q: Find the average value of the function g (t) = e' over the interval [0, 10].

A: g(t)=et over the interval [0,10]Average value of f(x)=1b−a∫abf(x)dx

Q: 2. Prove that (₁ + ²)" is convergent by using the Monotone Convergence Theorem.

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Q: Find the point on the line y = 4x + 2 that is closest to the origin. (x, y) =

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Q: 4-Z 4-z-2y k √ ₁² √²-²² ² -² -²y xyz²dx dy dz = 1 2 0 0 0

A: To solve for unknown.

Q: The average household received 24 pieces of mail each week. The number of bills and statements is…

A: The average household received 24 pieces of mail each week. The number of bills and statements is…

Q: Tonic 2: Functions The function f(x) = log10 (x-2) + 1 is given. a) Describe the transformations…

A: According to bartleby guidelines we are supposed to do only first three subparts . If you want more…

Q: tanh x = e²t - 1 e²x + 1

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Q: T Find the equation of the tangent to the curve = cos³x - sin²x at the point where x =

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Q: f(x) = −x+10 g(x) = x² − x − 11

A: Given that the function

Q: Determine the amplitude, period, and phase shift for the given function. - cos(2x - 5) y=1- 1…

A: To determine the amplitude, period, and phase shift for the given function.

Q: Consider the following graph of f (x). Which of the following are inflection points of f (x)? -3 O…

A: We have to find the coordinates of the inflection points from the given graph of function.Let's…

Q: Find the limit of the sequence: 5n²+8n+3 3n² + 8n +7 an

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Q: Using the Rules for Finding the Derivative of a Function. For the following exercise, assume that…

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Q: Please answer parts C and D

A: We have to find the limit of the given function.We will use the L Hospital rule to find the limit.

Q: Given the ellipse : 1 (x+2)² + (−1)² = 9 4 (a) Graph the ellipse, together with its major and minor…

A: The blue dashed line represents the horizontal and vertical lines passing through the center.

Q: 3. Sketch these functions and find their domain and range. a) f(x) = √√3x b) y = x³

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Q: 11. A car drives towards a 111 m skyscraper at 7.62 m/s. How fast is the car approaching the top of…

A: Given that :Height of the skyscraper =  mSpeed of the car =  m/sTo find :Rate of change of distance…

Q: Evaluate the limit lim x →0 O -1 1 18 1 9 √81-x-9 X

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Q: Find the area of the shaded region. r² = sin(20) P.

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