Give the Fourier transform of the function f. f(x) ha x € [0,₁] {* otherwise. =

Q: Determine if the improper integral •+∞ dx x ln7 x is convergent or divergent.

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Q: Iff and g are differentiable functions and h(x) = f(x)ex) , then K'(x) = rosen Fixe+fixie O [00+0000

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Q: Calculate lim X10 3x²-x-2 5x² + 4x + 1

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Q: Find the volume of the solid generated by revolving the area bounded by x² - 2kx - 4ky + k² = 0 and…

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Q: A rectangular field is to be enclosed with a fence. The available fencing material is 150 meters…

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Q: lim 818 sin n+1 n + sin n+2 n + sin n n+3 n +... + sin (2) = cos(1) - cos(2).

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Q: 2. Show the volume of the solid obtained by rotating about the x-axis the region 1 under the curve…

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Q: Consider the region bounded by y = ex+1, y = 1, and y-axis. 1.5 0.5 -1.5 -0.5 0 Which of the…

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Q: 2. Given the following: ƒ(x) = x³e¯*; ƒ'(x) = x²(x − 3)(− e¯¾); ƒ''(x) = x(x² − 6x + 6)e¯* a. Find…

A: Given

Q: Integral Calculus

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Q: Solve the following integrals: 1. S-7e*dx 2. (2ex - 6x) dx √² (3x) dx 3.

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Q: 6dx S: ³√x² x-

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Q: Evaluate the following integrals by interpreting each in terms of areas. (²√₁ 1 - x² dx Jo

A: Recall:  Area of circle=πr2

Q: Solve the integral. Show your solutions. Sỉ XUÂN ĐÃ

A: Given :∫13xe3xdx

Q: A small metal bar, whose initial temperature was 30° C, is dropped into a large container of boiling…

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Q: Evaluate 2 x√√x² + 4 dx.

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Q: Determine whether the equation is exact. If it is exact, find the solution. If the differential…

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Q: Express the repeating decimal as a fraction. 0.789626262626... 0.789626262626... =

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Q: BIN 2 sin² x cos x dx

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Q: True or false: If {(2, 1-z, z+3)} is the solution set of a system with dependent equations, then (0,…

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Q: ve for y esec(4y²-6y+14) = 3x + 1

A: We have to solve for y of the given equation

Q: Find a cubic function y=ax³ + bx² +cx+d that has a local maximum value of 3 at -2 and a local…

A: According to our guideline the answer to answer only the first question if you want any particular…

Q: A car is moving with uniform acceleration. it covers 200 m in 2 sec and 220 m in next 4 sec. the…

A: A detailed solution is given below.

Q: The particular solution In (x) = 3x + 4y, y(0) = 0 is A. e³x + 3e-4y = 4 B. 4e3x3e-4y = 3 C. 4e3x +…

A: Topic = Differential equation

Q: Let A= de ghi Assume that det(A)=-11, compute the following. NOTE: Enter all values exactly. (a) (b)…

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Q: Solve the following LONG DIVISION 6x³5x249x equation by using + 60 = 0

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Q: To estimate the height of a building, two students find the angle of elevation from a point (at…

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Q: Q3- Sketch the region of integration and evaluate the integral: In8 lny ex+y dxdy 0

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Q: f(x csc² 2x - x cos 2x)dx

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Q: Calculate Differentiate. 1 = 2 z² + 1 f(z)

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Q: Consider the initial value problem y' + y = 5 + 2 cos 2t, y(0) = 0. 4 a) Find the solution of this…

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Q: . Find the area bounded by the given curves. y = 9x² and the x - axis.

A: First we find point of intersection of curve y=9-x2 and x-axis. Put y=0, 0=9-x2 x2 =9 x=±3 Therefore…

Q: Evaluate In x x (4 - In² x) - In 14- In² x | +C - 2 In 14-In² x | +C 12 -dx In | x (4- In²x) | +C In…

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Q: Consider the arc L: y = 1+ cosa from (0, 2) to (,¹). of the surface formed when I is revolved about…

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Q: 3) Given y(0) = 1 Over what area are we guaranteed a unique solution? Explain using existence and…

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Q: 26. b) Given four points A(-2, 0, -3), B (1, -2, 1), C (-2,-3,2), D ,0). Find the equation of the…

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Q: Q2. If f(x, y) = xy² + y²cosy + xsiny then a) y² - siny c) 2y + cosy a²f is дудх b) y² + cosy d) 2y…

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Q: D) Find the parametric and symmetric equations of the line through the points (1,2,0) fic and sym of…

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Q: What is the mass of body if the exerted force of 10 N is accelerated by 5 m/sec^2? O 4.5 kg O 1.5 kg…

A: Find mass of body

Q: 4. 5. 1 X√(x)}² (x)²-49 dx 1 √9+8x-x² dx

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Q: 6dx X – - 3√/x²

A: Given

Q: or each function h(x), find two functions f(x) and g(x) such that h(x) = f(g(x)) a) h(x)=√x² + 3 b)…

A: Topic:- function

Q: a. Verify that the given point lies on the curve. b. Determine an equation of the line tangent to…

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Q: interval of convergence. b. sin² x

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Q: (2x²9x9)dx x3 x³ - 9x

A: Here we have to do partial fraction and after that integration

Q: Solve the integral shown below. JT fsins 2x cos7 2xdx

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Q: Calculate √√3 8 2 1/√3 1 + x² dx

A: Given ∫13381+x2 dxTo evaluate the integral:

Q: 1 Consider the function f (x) = on the interval X - 1, 1]. If the Mean Value Theorem can be applied…

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Q: The binary operation defined as a+b=3a - 2b is closed in all the given sets EXCEPT set of Natural…

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Q: Example 3: Find the parametric and symmetric of the line passing through the point (-3, 5, 4) and…

A: Here, the given equation of the line is: x=1+3t,y=-1-2t,z=3+t Therefore, the direction vector is:…