Evaluate each of the following definite integrals 4 |x- 3| dx (x2 - х) dx х2 +x+1

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A: The Right end point approximation formula is: ∫abf(x)dx=∆xf(x1)+f(x2)+f(x3)+...+f(xn) Divide…

Q: Find the extreme value/s of f(x) = 4 sin² x − cos 2x on - (327 3π 5π " 2 2

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Q: 11. The arc length of the graph of a function f(x) on the interval [a, b] is defined as follows. L =…

A: Arc length of Function

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: Consider the curve parametrized by x = t4 + 1 and y t6 + 4t5. www dy a) Find in terms of t. dx b)…

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Q: Determine whether the series converges. 1 k+11 The series

A: The given series,    ∑k=1∞1k+11

Q: Suppose that f(x, y) is differentiable at the point (3, 1) with f(3, 1) = 4, fx (3, 1) = 2, and fy…

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Q: Consider the curve parameterized by x(t) = 2(t²-1), y(t) = 5e²t, tER Determine an equation of the…

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Q: Consider the curve parameterized by x 3t2 3 and y 2t°. Find equations for all tangent lines to this…

A: Here we have to find the equation of tangent line.

Q: a) Find a polynomial P(x)= a + a₁x+0₂2² +03x³ +ay 20² +a5 205 of degree 5 such that as = 1, and…

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Q: 3. A container in the shape of a (right) cylindrical can with an open top of volume 87 cm³ is to be…

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Q: Suppose that f(x) = -9x/6. Evaluate each of the following: f'(2) = f'(5) =

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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: Verify Green's Theorem by evaluating both integrals y² dx + x² dy = / dA дх ду for the given path.…

A: Here we have to verify the Green's theorem.

Q: 2. Evaluate the indefinite integrals. (a) fx² - 2e*dx (b) Evaluate (3-4x)¹5 dx

A: We have to evaluate the indefinite integral

Q: y? = x and y2 = 2 – x %3D

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Q: _4 JA 2 -D 2 CH

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Q: -8 27 -6 -5 -4 -3 -2 ਆਰਡਰ 41 3 1 -2 -3 The curve above is the graph of a sinusoidal function. It…

A: Given query is to find the graph of the function.

Q: 13. One group of teenagers bought 8 deluxe burgers, 6 orders of fries, and 6 large soft drinks for…

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Q: he conclusion of Green's Theorem by evaluating both sides of each of the two forms of Green's…

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Q: 9. Using first principles, determine the equation of the tangent line at point (2,2) on the curve…

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Q: 3. [_x dx √2 +*

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Q: Find the surface area when the curve C = {(x, y): 0 ≤ x ≤ 2, y² = 2 − x} about the x-axis.

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Q: 1. Determine the following using the graph off provided below. If the value is infinite, specify oo…

A: x→a+ means; x approaching to value a from the right side.Equation of straight line:(-7, 3) and  (1,…

Q: X 0 2000 A television camera at ground level is 2000 feet away from the launching pad of a space…

A: Solution is done in step 2

Q: 1 Rewrite the logarithmic equation log4 16 -2 1 Gr= 16 04² = 21/160 4-2 4²/16--2 416 = -2 4-2= O O =…

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Q: (-0.7, 0) -0.5 (2-1) 2 ده - د.0 - گا - 2t (0.7,0.2) (1.5.2) ۱۰

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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: The rate (in liters per minute) at which water drains from a tank is recorded at half-minute…

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Q: Find an equation for the tangent line to the curve parametrized by x = 4t y = est at the point t =…

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Q: Use the Fundamental Theorem of Calculus to find the "area under the curve" of -² + 7x between x = 2…

A: The region is bounded by -x2+7x between x=2 to x=5

Q: Find the absolute maximum and absolute minimum values off on the given interval. (Round all answers…

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Q: Find the following using the table below. x 1 2 3 4 4 2 f(x) 1 3 f'(x) 2 3 4 1 g(x) 13 4 2 g'(x) 2 4…

A: Chain Rule of differentiation : fgx' = f'gx .g'(x)

Q: Find the arc length L of the graph of r(t). r(t) = 5 cos(t)i + 5 sin(t)j + tk, 0 <t < 2n L

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Q: . Find an equation for the surface area of the rectangular box. =(x, y) dy = . If the surface area…

A: We will solve the surface area problem.

Q: Determine the positive and negative intervals of the polynomial function P (x) = x(x − 2)(x + 2)(x +…

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Q: d d Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: Use the indicated method to approximate the area under the curve f(x)= x³ +28 on the interval [-3,…

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Q: Calculate the definite integral by referring to the figure with the indicated areas. [f(x)dx a Area…

A: topic - definite integral area above the x axis is taken as positive in definite integral when…

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1. dy

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Q: QUESTION 8 If you save $270 per quarter for retirement in an account that earns 8% interest per…

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Q: ectile is launched straight up in the air. Its height (in feet) t seconds after launch is given by…

A: Given query is to find the velocity at indicated point.

Q: Evaluate (2x - y) dx + (x + 6y) dy. C: x-axis from x = 0 to x = 5

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Q: Set up, but do NOT evaluate, a triple iterated integral of the function f(x, y, z)=x+ z over the…

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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: L(25 — х?)3/2. |dx

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Q: Consider the following theorem. Theorem If f is integrable on [a, b], then [ºf(x) dx = dx = lim…

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Q: The traffic flow rate (cars per hour) across an intersection is r(t) = 200 + 1000t - 150t², where t…

A: To find out the numbe of cars pass through the intersection between 6 am and 11 am.

Q: The total cost (in dollars) of producing a golf clubs per day is given by the formula C(x) = 450 +…

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Q: Write the integral in terms of u and du. Then evaluate. u = 812 + 1 (Use symbolic notation and…

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