Evaluate the definite Integral by the limit definition. (x2 + 4) dx

Q: 5 Describe the right-hand and left-hand behavior of the graph of the polynomial functions. a) f(x) =…

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Q: Solve the following differential equation y"+2y' +y=x-1 Select one: O a. YG.S= Ce¯+c,e¯2x+x-3 O b.…

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Q: Find the area bounded by the curve y= 4-x2 and thex-axis. Graph

A: We can find the area bounded as below.

Q: Find an equation of the sphere whose endpoints of a diameter are (−2, 0, 5) and (−1, 2, 3). Show all…

A: Here we have to obtain an equation of the sphere whose endpoints of a diameter are (−2, 0, 5) and…

Q: (1) Which is the correct formula for finding the derivative of the product of two functions? O (fg)'…

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Q: Use the integral test to determine whether the series converges. Σ 4n - 1 n=1 converges diverges

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Q: A cylinder (round can) has a circular base and a circular top with vertical sides in between. Let rr…

A: Given ,  A cylinder (round can) has a circular base and a circular top with vertical sides in…

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

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Q: Demand Function: d(x)= 500-0.6x Supply Function: s(x)= 0.2x Find the Equilibrium quantity= Find…

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Q: E. Find the value of D, E, and F of the following circle that passes through (-1, 4)(3,2) and (5,2)

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Q: 7) At the right is the top view of a Chemistry Butiding in UP Diliman. It resembles the famous…

A: The sum of a polygon's internal angles: The following formula is used to determine the sum of…

Q: Use Newton's Method to approximate the root of x In r 2 accurate to five decimal places. Begin by…

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Q: 8. True or False: If lim an = 0, then an converges. %3D n=0 (a) True (b) False

A: Solved below

Q: Consider the graph and determine the open intervals on which the function is increasing and on which…

A: Observe the given graph and decide whether function is increasing or decreasing.

Q: An advertising agency spends £x on a newspaper campaign and a further £y promoting its client's…

A: The Multiplier Method of Lagrange We may need to maximize (minimize) a function that is constrained…

Q: Directions: Prove the following statements. 1. If f(x) = (x² – 1)3 then f'(x) = 6x3 – 12x + 6x.

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Q: Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the…

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Q: 2x – 6 X + 3 If f(x) = { x- 3 then the li X 5 X = 3 a. 5 b. 1 С. 2

A: Given for x = 3 , f(x) = 5

Q: g(x) If f(x) then h(x)'

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Q: Find the area of the region. See Examples 1, 2, 3, and 4. f(x) = (x – 5)3 g(x) = x - 5 y 1.5| 1.0…

A: This question can be solved using the concept of area under curves.

Q: If f(w) (3w), find f'(w). Use exact values. = COS f'(w) =

A: We can find the exact answer as below.

Q: Is the area under the curve y (Inx)/x from X-1 to X=x finite? If so, what is it?

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Q: 2. ydx + (3x – xy + 2)dy = 0

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Q: Consider the function f(t) = 6 sec (t) – 6t°. Let F(t) be the antiderivative of f(t) with F(0) = 0.…

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Q: b). Determine if y =x tan (x) satisfy dy_y x sec²(x) = 0 when y|x=0 = ( | dx

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Q: Consider the differential equation xy" + 3xy' - 3y = 3x - 2x. (a) Verify that yi = x and y2 = x…

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Q: 5. Given y=af(1 Find when =1 if f(2) = tand f(2) = 5.

A: Topic = Derivative

Q: - 9 sin(3x) and f'(0) Given f''(x) f(0) = 1. 3 and Find f(-

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Q: D. Find The or mogonal traectory of the family f aurves y=

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Q: Given f''(x) = 8x + 6 and f'(0) = 1 and f(0) = 2. Find f'(x) =

A: f''(x)=8x +6integrating w.r.t. x;∫ f''(x) dx =f'(x)f'(x) =∫ (8x+6) dx        =8x22+6x+Cf'(x)…

Q: Determine the convergence or divergence of the series. n = 8 converges diverges

A: Given query is to find series converges or diverges.

Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

A: Draw the region and use the washer method of finding the volume of revolution of solids.

Q: Is 3 A m, m being any real number, possible? Explain. [IC]

A: This is a problem related to vector parts. Based on the general formula and concepts we will answer…

Q: (E – 4)A^ = -글Vyy-3), 1sys 25 ter a fraction, integer, or exact decimal. Do not approximate.

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Q: . Find the point(s) on the graph of the curve f(x)= x 3 /3 +3x+4/x the tangent is horizontal

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Q: For the function y f(x) - la + 10: - df at x = 1. dx a. Find f'(1) = b. Find a formula for x =…

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Q: Determine if the geometric series converges or diverges. If it converges, find its sum. 24 3 4 + 1+…

A: Given query is to find series converges or diverges.

Q: A firm estimates that it will sell N advertising, where dollars. Use the derivative to find the…

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Q: How do you do optimization in calculus? List all steps

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Q: Find the derivative of the function. 4 - 4x – x2 f(x) x2 - 6 — 4х — 2 - -1+ f'(x) = -x – 6

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Q: Solve using product rule d(uv) = u dv + v du: f(x) = (3x^2 – x + 4) (2x^2 – 1)

A: Our Aim is to solve the given function using the Product Rule where f(x)=(3x2-x+4)(2x2-1)

Q: 2x2 -9x Find the limits and justify if needed. 12. lim x² – 1 X-

A: Given query is to find the limit of the expression.

Q: (a) On what intervals is f increasing? (Enter your answer using interval notation.) On what…

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Q: Since the start of July, OHaganBooks.com has seen its weekly sales increase. OHaganBooks.com fits…

A: For (a), w'(t)=36t2+252t+6242' =72t+252 For (b), For t=1, w'(1)=72+252=324

Q: Consider the function f(x) = 4x° + 7x³ – 9x? – 1. An antiderivative of f(x) is F(x) Ax" + Bx" + Cx²…

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Q: Problem 2: Given a function 4x -1 f(x) = 2x +1 Use tabular method to determine if the limit of a…

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Q: QUESTION 3 Find a formula for the nth term of the sequence. 1, 4 9' 16 25 (reciprocals of squares…

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Q: What is the value of c? If we try to apply Rolle's Thorem to the function f(x) = 2x? – 20x – 2 on…

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Q: 5. Which of the following is (a) n! n=1 80 (b) n=1 (c) E T=D1 (d) -1)" (2n)! T1

A: We have to find out the power series

Q: We have found that the partiaular solution of the height function is s(t) = -4.9t + v(0)t + 3 and…

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