1. Do the following converge or diverge? Evaluate it if it converges. Justify your claim. (i) St=10 In r √√x dr.

Q: Exercises: 1. J- (x-4) (2x+3)(2x+1)

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Q: 3. Given 5y +4x² = 4x-y, find: dy dx a. b. d²y dx²

A: Derivative

Q: A candy box is to be made out of a piece of cardboard that measures 8 by 12 inches. Squares of equal…

A: Solution: Let the side of the square = x Given : Length of cardboard = 12 inches Breadth of…

Q: A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight…

A: To solve the following problem

Q: 14. Given f(x) = ax+b b-ax a. What is the root of f(x)? X b. What is the equation of the function's…

A: Given function:- fx=ax+bb-ax

Q: Give the function f(x) = ₁ Evaluate the one-side

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Q: Let f(x) Tangent line: y = X 5 - 4 +4 Find an equation for the tangent line to the graph of f at x =…

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Q: 4x+10 (x-2)(x²-2x+1) dx

A: A rational function of the form px+q(x-a)(x-b)2 can be broken into partial fraction…

Q: Consider the function f(x) Then A= and B Then C = For each of the following intervals, tell whether…

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Q: Use implicit differentiation to find the following. (If only the x-coordinate is given, you must…

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Q: dx 2.) √ 8²x+1 €2x+1

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Q: Which of the following statements is incorrect? A) If a, converges, then n=1 n=1 22 a, also…

A: The incorrect statement is (D) If lim n -> ∞ a_{n} = 0, then is absolutely convergent. This…

Q: Determine whether the sequence is increasing, decreasing, or not monotonic 3n - 4 4n+ 5 an O…

A: Given expression an = 3n-44n+5

Q: Let x be a number. Translate the English phrase into a mathematical expression. 13) The total of -78…

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Q: Find the inverses of the matrices in Exercises 29-32, if they exist. Use the algorithm introduced in…

A: (29)  A=1247if  A=abcdthan A-1=1ad-bcd-b-ca

Q: How do you find these?

A: Here we have to find the extrema of the given functions.

Q: Y 2x - 3 r2 _ 5x +6 2x - 3 Jo x2 – 5+6 dx = 4 ln 2 – 3 ln 3.

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Q: Apply the Hamilton-Hare (HH), Jefferson-D'Hondt (JDH), and Webster-Sainte-Lague (WSL) methods to…

A: Hamilton's Method involves the following steps 1) Determine how many people each representative…

Q: (a) Differentiate the function below with respect to . 1 y (-72²+62+5)* Note: • In Text mode the…

A: Please see the below picture for detailed solution.

Q: Drag and drop the given determinant ratios of x and y Then Drag the final answers of x and y x 2 19…

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Q: f"(x) = 8x - 5 and f'(0) = 4 and f(0) = 3. Find f'(x)= = and find f(1) 4x² - 5x+4 -32 =

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Q: Σ(-1)¹+¹, n=1 Σ;(3) n 2 n=1 n=2 1 nlnn n 1 2n+1 I only II only III only I and III only I, II, and…

A: To solve the following problem and find which of the series converges

Q: Find and the slopes of the tangent lines shown on the graph of the polar equation. (If an answer…

A: Given curve equation:- r=21-sinθ

Q: f(x) = sin 'x Sin'x -2x

A: We have to find the critical point.

Q: x²y + xy² where x = s² and əz Let z = x y = t³ then Answer: ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ əs at t = 1 and s =…

A: Given:- z=x2y+xy2 Where x=s2 ,y=t3

Q: Does the following power series converge for all real values of x? Σ n=1 xn nn No it does not…

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Q: Differentiate the function below with respect to a. f(x) =ln (−4 x² − 5 x + 8) Note: • In Text mode…

A: Given function is f(x)=ln(-4x2-5x+8)

Q: d. lim 1³. ³+1 - 1 x-1X

A: according to bartleby guide line we do only first part of multiparts questions (d)…

Q: If ƒ (x) +x5(ƒ (x) )² = 34 and f(1) = 2, then f'(1) =

A: Derivative

Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) =…

A: The given function fx=ln x on the interval 1, 9. We have to check the function satisfies the Mean…

Q: Suppose that f(x, y) = 6, and D = {(x, y) | x² + y² ≤ 1}. 2 Then the double integral of f(x, y) over…

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Q: 1/2 -1/2 4(8 + x)¹/² − x(8 + x)¯¹⁄² 8 + x

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Q: Two days after he bought a speedometer for his bicycle, Lance brought it back to the Yellow Jersey…

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Q: dx Assume that x = x(t) and y = y(t). Let y = x³ +6 and=3 when x = 1. dy Find when x = 1. dt dy dt…

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Q: -1 a) Given y = x 2, differentiate y with respect to x. Enter your answer in syntax

A: According to Power rule if  y=xn  then y' = nxn-1

Q: The owner of a local cinema is considering a plan for renovating and improving the theater, which…

A: Given:  The net income by the end of 3 years is given by  ∫03510,000e-0.1t dt-190,000 To Find:  To…

Q: ve nd in on nd (3) in -ly en he is ust in Find the inverses of the matrices in Exercises 29-32, if…

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Q: If lim f b→∞ 1 xp (A) (C) b dx 1 пр n=1 (E) (B) Σ diverges пр n=1 1 NP- n=1 is finite, then which of…

A: Given that limb→∞∫1bdxxp is finite. We have to find the true statement from the given.

Q: If 46 +3ƒ(x) + 5x²(ƒ(x))³ = 0 and ƒ(−1) = −2, find ƒ'(-1). f'(-1) = 0

A: Given46+3f(x)+5x2f(x)3=0f-1=-2   We are required to findf'(-1)

Q: Use matrix inversion to solve each collection of systems of linear equations. HINT [See Example 4.]…

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

A: We need to find the limit of the sequence.limn→∞cos2n3n

Q: Consider the graph of a function f on the interval [0,4]. y 10 8- 6+ 4 2 0 1 2 3 4 -X. Identify all…

A: 1) It is given that the graph of the function f on the interval 0,4. It is known that x=c is a…

Q: Use a graphing utility to graph the curve represented by the parametric equations. (Indicate the…

A: The given parametric equation is: x=6cos3θy=6sin3θ  Use a graphing utility to graph the curve…

Q: The position of a particle moving along a coordinate line is s= √70+ 6t, with s in meters and t in…

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Q: For what values of x is the tangent line of the graph of parallel to the line y = x − 1.1? - ƒ(x) =…

A: As per guidelines, we can solve only first question if multiple questions are posted. Please repost…

Q: Integral using Evaluate the Integral of and odd functions even T1/2 Se _T1/2 Sin x Cos x dx соб the…

A: L=∫-π2π2(sinx.cosx)dxfrom property ∫-aaf(x)dx=0, if f(x) is odd2∫0af(x)dx, if f(x) is even

Q: Find two numbers differing by 42 whose product is as small as possible. Enter your two numbers as a…

A: We can solve the given problem by using the second derivative test.

Q: Determine whether the sequence is increasing, decreasing, or not monotonic. an = 7n + 1 n O…

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Q: Integrate sinx given integral by 20 2 w5 x= sing the using sin: 1 + si

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Q: Find the cross product of the unit vectors. jxi -k X Sketch your result. k t -k O k 't

A: Given that , j×i find the cross product.