Is g(x) = ln( x2+2 ) uniformly continuous on the interval (−∞,∞)?

Q: et [a, b] be a real interva b]→X is continuous, the is continuously differentia

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Q: Determine if the improper integral converges or diverges: 1 dx. 1+x²

A: Our Aim is to determine whether the improper integral given below converges or diverges∫0∞11+x2 -(i)

Q: 1 Prove that the integral : Tz dx is convergent. 1+x

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Q: dx (x– 1)%

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Q: Determine whether the improper integral diverges or converges. dx 1. (2х-1)3 dx 2. x +1

A: No.2 The improper integral is of second kind where f(x) = 1/(x+1) has one point of infinte…

Q: Suppose that Xis a continuous unknown with -4< X< 4  having PDF denoted fsatisfying f ( x ) = c (…

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Q: dx x2 – 1

A: Given: ∫02xx2-1dx

Q: Express the limit as a definite integral on the given interval. n lim x, In(2 + x,-) Ax, [0, 4] i =…

A:

Q: x° e* dx 00

A: Given : ∫-∞0x5exdx

Q: Is f(x) = ln(x) uniformly continuous on (0, 1)? Justify your response.

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Q: Determine whether the improper integral diverges or converges. dx 1.f (2x-1)³

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Q: F(x)= ]7+1 3x t dt 2 F'(x) = %3D

A: We will find the derivative using Fundamental Theorem of Calculus.

Q: If the integral diverges, indicate that using the checkbox. 6 dx The integral diverges x(x + 1)

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Q: Show that integral 0 to infinity e -x 2 is convergent.

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Q: –1 dx x V In (-x) -3

A: Find the type of the generalized integral and examine its convergence.…

Q: Determine whether the improper integral diverges or converges. 1 dx e2x + e-2x

A: Evaluate integral,

Q: Determine whether the improper integral diverges or converges. dx 1.co (2x-1)* 00 dx 2. x +1

A: To check weather the given Integral is converges or diverges.

Q: Show that In(x") = y In(x) for all x, y > 0, only using the rules of derivative for the natural…

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Q: 4) Determine whether the integral converges or diverges, and if it converges, find its value. - dx…

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Q: •4 x dx 10 x2 – 9

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Q: 10. Determine whether the improper integral converges or diverges 3 dx (x – 1)3 -

A: Given query is to integral converges or diverges.

Q: b. It is known that on the integration interval -1 <x< 3, for the integrand function f (x): 2.2 <…

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Q: Express the limit as a definite integral on the given interval. n X;* lim -Ax, [1, 9] (x;*)2 + 8 i =…

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Q: Сompute f dx, where f(x)=|x|.

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Q: sin (nx +3) S,(x) =- is convergent point wise to zero function. %3D п - 1

A: First one is true second is false.

Q: The integral of ƒ In(ln(x))dx can not be expressed as a finite sum of functions. What do we call…

A: It is called as non elementary integral

Q: Determine if the integral converges or diverges by comparison.

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Q: Find the interval in which function f(x)=sin (log,x)+cos(log,x) is decreasing

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Q: Determine whether the integral  integral  1 to infinity (1/x) dx is convergent or divergent

A: We will use the fact that

Q: 353, Without integrating, determine whether the integral dx converges or diverges by comparing the…

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Q: Explain why the improper integral (x + 3) sin(x) dx L. (x² + 1)(x² + 4)² is convergent. 8

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Q: calculate the limit of ln(x) - (e)^x  x goes to + infinite

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Q: An odd piecewise continuous function f(x) on every finite interval of (-0, 0) such that / fx)| dxis…

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Q: Determine whether the integral is convergent or divergent. `"e-1/x dx convergent divergent

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Q: 4. (a) Explain why the integral (1+ x)3 dx is an improper integral. Determine whether the improper…

A: We have to find out

Q: 1 dx is convergent x" If n>2, the integration

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Q: Determine whether the integral is convergent or divergent. *e-1/x dx x2

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Q: Linearize f(x) = 5 cos x about x = pi over 2. f(x) = -5x

A: linearization around x=a is given by :L(x)=f(a)+f'(a)(x-a)

Q: An even piecewise continuous function f(x) on every finite interval of (-oo, 0) such that :/ (x)|…

A: The given statement is : An even piecewise continuous function f(x) on every finite interval of -∞,∞…

Q: .2 x+15 dx Jx* +3 1

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Q: 1 Determine the convergence of the integral | dx. (2 – x)

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Q: 55. Show that dx J+4 converges by comparing with x³ + xdx. -3 dx. х

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Q: Evaluate if the integral converges 1. 1. dx (x-1)7 , sin x dx 3. dx 2.

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Q: Express the limit as a definite integral on the given interval. n x* lim (xF)2 + 2 Ax, [1, 7] (x*)2…

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Q: Determine if this improper integral will diverge or converge dx (x² – 1)4/3 1 Apply this in solving:…

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Q: b) Determine whether the improper integral `1+ sin r -dx 1+x² converges or diverges.

A: Comparison test :  Suppose for x&gt;a  . If converges then also converges . If diverges then…

Q: Only piecewise continuous functionsf (x) on every finite interval (0, 0) such that 00 | S(x)| dxis…

A: According to the condition of convergence for Fourier integral,  Let f and f' be piecewise…

Q: (b) Explain why the integral e- *x* dx is convergent.

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Q: Determine if the integral x dx To x² – 9 converges ?

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.