Evaluate the following definite integrals using special techniques for integration: (x³) dx /(x²+1) J(x²+2x-1) dx/ (3-x) J(x4+x³-2) dx/(x²+5) J (e2x + 1) dx / (ex + 1) J (x² - 2x + 1) dx/(x + 2) J (x² + 2x + 1) dx/(x² + 2)

Q: ƒ (t) = -{ 5,03

A: We know the followingLf(t)=∫0∞e-stf(t)dtLeat=1s-aLtn=n!sn+1Lsinat=as2+a2Lcosbt=ss2+b2

Q: B: Solve the following integrations: a- [x³e-2x¹ dx b-fdx +10 c-f3sec³x. tanx dx arks

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A: Solution is given below:

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A: Explanation of the answer is as follows

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A: We have to find the given series is convergent or divergent  , if the series is convergent give its…

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Q: *²+√** dx x2

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A: Find out the domain of the function.

Q: ·1₂ 3. 1³-x²+2-1 dz

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A: The given curves are; y=6-x-x2 and x-axis or y=0.   Now find the x-intercept of the the curve…

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Q: Prove the limit below exists, by using the Binomial Theorem and the Monotone converge ONLY. Do not…

A: Prove the limit below exists, by using the Binomial Theorem and the Monotone converge ONLY. Do not…

Q: (5) f(x) = cos (5 - 2x) (7) f(x): = cos (√x³ + 1) (9) f(x) = cot (x5) (6) f(x) = cos (4x7 + 3) (8)…

A: as per company guidelines we solve only first three subparts when multiple parts question being…

Q: Question 1. A critical point of the function g(x, y) = ex y + 3x²y-y is (0,0). Use the Second…

A: Explained below

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A: As per our guidelines we are allowed to answer only three subparts of a given question. Kindly…

Q: this is incorrect please resvole

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Q: Draw the function y = √x-8

A: The 5 points are the following.

Q: Graph the linear inequality. 4x-y < 4 CIB Use the graphing tool on the right to graph the…

A: Here we will draw inequality,

Q: Find the location and value of each local extremum for the function. 28) + -3 3 -4 -M

A: To find location and value of each local extremum of given function.

Q: Q2.B. A bag contains 19 tickets numbered from 1 to 19. A ticket is drawn and then another ticket is…

A: Given that, A bag contains 19 tickets numbered from 1 to 19. A ticket is drawn and then another…

Q: z²+1 5. S ₂²³(x+5) I

A: Let's solve given integral.

Q: What is the area of the region bounded above by y = -3 MX. 54-3-2-1 1 2 3 4 45 O ভাল লাল নাল O O O…

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Q: Use the method of undetermined coefficients to find a particular solution x" + 8x' + 9x = t³ Xp²

A: Solution of given question is written in below steps.

Q: 9. Integral (2x-5) dx x²5x+3

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Q: Evaluate the following triple integral by hand: 2 √z } } } - dxdydz = 3 z=1 y=2 x=-1 X y

A: Topic = Integration

Q: Q1/ Determine the interval of convergence and the radius for the following power series (x - 2)" Σ…

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Q: Solve the following initial value problem completely, and check your answer by comparing it to the…

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Q: Determine the area enclosed by y = from x= -3/2 to x = 1. |- 1 x+2 and y = (x + 2)²

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Q: The length of an astroid The graph of the equation x2/3 + y2/3= 1 is one of a family of curves…

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Q: Find the average value of: f(x) = 8 sin x + 3 cos x on the interval [0,1] 3 Average value =

A: Solved below.

Q: Given the functions: f(x)=x²³-8x g(x) = √2x h(x) = 6x+7 Evaluate the function h (f(x)) for x = 3.…

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Q: X f(x) g(x) -2 5 1 -1 2 3 0 4 1 -2 2 -4 -3 -6 -1 f'(x) -4 -2 1 5 -5 g'(x) -1 3 -3 4 2

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Q: Give the component form of the vector represented by the directed line segment from (4, 5, 6) to (4,…

A: See this  solution in below

Q: The solution of differential equation y' + (cotx) y = 3 sin x cos x, x=(0,7). is:

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Q: Find a vector-valued function, using the given parameter, to represent the intersection of the…

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Q: 12.) S³ S² (3x - 2y ¹) dy dx

A: according to company rules we can answer only the first question and rest can be reposted.

Q: 7.(a) f(x) tan (In x) + 52 7.(b) f(x) = log2 (tan r) + In (¹)

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Q: What is the polar equation of a circle of radius a centered at the origin? Use this equation to…

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Q: -1.5 -4.5 -1.5 Let [ f(x)dx = 5, |_^*^* f(x)dx = 6, [*¹*³ f(x)dx = 5. -6 -6 Find and -3 [²₁ f(x) dx…

A: This question is related to definite integration, we will solve it using given information.

Q: Find (f+g)(x) and identify the graph of f+g. f(x)=x² and g(x) = 5 Part: 0/2 Part 1 of 2 (f+g)(x) =…

A: As per our company guidelines we can answer only one question at a time so if you need more answers…

Q: The solution of differential equation y' + (cot x) y = 3 sin x cos x, x = (0,π). is:

A: Using Integrating Factor formula: