Show that a sequence of Riemann-Integrable functions fn(x) converges uniformly to Riemann-integrable function f().

Q: How to prove {sin(n)} is a bounded seuqence that does not converge?

A: To prove xn=sinn is bounded. By definition, a sequence xn is bounded if it is both bounded above and…

Q: Determine whether Ln=1 n2+1 tan- is convergent using integral test.

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Q: Enter its finite) value if its 5. a) I5 the generalised integral convergent or divergent?…

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Q: how that fuGe)= x" (1-x") converges bintwise # se G, 1]. Is fn G) Thyenges %3D uni formly?

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Q: 1 Determine if the integral [Inxdx converges or diverges. 0

A: Given problem:- Determine if the integral ∫01ln(x)dxconverges or diverges

Q: 4 dx

A: Use limit comparison test and p series test

Q: 12. Determine whether the improper integral dx converges or diverges. Show all work.

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Q: Determine whether converges absolutely, converges condi- 2" cos n n=0 tionally, or diverges.

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Q: Determine whether the integral is convergent e-2P dp convergent divergent If it is convergent,…

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Q: dx 2. x +1 -1

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Q: Is Uniform convergence of {fn(x)} is sufficient but not necessary to transmit continuity from the…

A: From the theorem stated in step two, we can see that the function is uniformly continuous and we can…

Q: 2. Determine whether the given improper integral diverges: converges or

A: We know, ddxx = 12x ddxx = ddxx12 = 12x12-1 = 12x-12 = 12x12 = 12x   Also we know, ∫ex dx = ex+C

Q: Compute the 9th derivative of f(x) = arctan at x = 0. f(0) = %3D Hint: Use the MacLaurin series for…

A: Solve for derivative

Q: 5. Use the Comparison Theorem to prove whether the integral converges or diverges. 2.x 2.x3 +7

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Q: Let fn : [-3, 3] → R be defined by fn(x) = x2n x2n+1 Does {fn(x)} converges uniformly on [-3,3]?…

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Q: A sequence of non zero functions fn a nonzero function f both defined on (0, 1) such that fn 1 does…

A: See the attachment.

Q: 10. Determine whether | sin(x)dr converges or diverges. If this improper integral converges,…

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Q: If fn is a uniformly equicontinuous sequence of functions on a compact interval and fn → f…

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Q: Let f_n(x)= nx / 1+nx^2.  Find the pointwise limit of (f_n) for all x in (0,infinity). Is the…

A: Given : fn(x)=nx1+nx2 .

Q: Show that f„(x) = x" (1– x") converges pointwise V x € (-1,1]. Is f„(x) converges uniformly?

A: When a sequence includes a variable, it becomes a sequence of function. A sequence of function can…

Q: The values of a that make the integral Tdx converges

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Q: Let (fn) be a sequence of differentiable functions defined on the closed interval [a, b], and assume…

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Q: (b) Give an example to show that the product (fngn) may not converge uniformly.

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Q: Does sin () x 7 converge or diverge? Why?

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Q: Perform a test to determine if it converge or diverge -1 x 2sin 1 dx 1– x -1

A: The function is given by: ∫-112sin-1x1-xdx If the function fx=2sin-1x1-x is positive, continuous and…

Q: 1 dx et+ e

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Q: Determine whether the integral is convergent or divergent. e-vy dy convergent divergent If it is…

A: Here is the solution of the given problem.

Q: Find the n-th partial sums, S,, in order to find the upper Riemann sum for (-4x+2)dx

A: Let, the given interval [a,b]=[0,3] be divided into n sub-intervals such that the width of each…

Q: Let (hn),(tn) be sequences of bounded functions on A that converges uniformly on A to h,t…

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Q: A. converges B. diverges

A: Given that the series: A. ∑n=1∞15n B. ∑n=1∞n+6n2+12n+4 To find check the series converges or…

Q: Determine if the integral o 1acaz da is convergent or diver- gent. If it is convergent find its…

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Q: 1 Test the convergence of fsin x dx.

A: To check convergence of given integral use comparison test of integrals. Comparison test: For two…

Q: Determine whether integral 0 to pie /2 sec x dx    converges or diverges

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Q: Test the convergence of sin dx.

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Q: Show that a sequence of Riemann-Integrable functions fn(x) converges uniformly to Riemann-integrable…

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Q: prove convergence or divergeence A) is similar to E by using the Limit Comparison Test tan B)…

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Q: value of for which Are there cmy value f converges.

A: We know that a series is said to be convergent if the sequence of its partial sums converges. Using…

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

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Q: Check the convergence of : xe-*dx

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Q: In x Determine whether the improper integral dx converges or diverges. If it converges, find its…

A: To find the following problem

Q: A sequence of differentiable functions fn where fn converges uniformly and fn does not converge…

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Q: Only piecewise continuous functions f(x) on every finite interval (0, ∞) such that F(x)| dxis…

A: The given statement is false.

Q: 1) Determine if the following integral converges or diverges. If the converges determine its value.

A: we use integral test to find out converges or diverges

Q: Examine the convergence of the integral.

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Q: The sequence (Xn) = (1, 3, 1, 3, 1, . . . , 1, 3, ...) is: Converge to 3. O Divergent. Converge to 0…

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Q: (2 - de using limit of the Riemann sum.

A: First, find the width and height for the rectangles. Let the number of the intervals be n = 4. The…

Q: Determine if the improper integral converges and if so, find the value it converges to. Use…

A: Given Data: Integral: ∫1∞1xxdx Using integral test, Rewrite the integral. ∫1∞1xxdx=∫1∞1x32dx

Q: 5. a) 15 the generalised integrel -X dx convergent or divergent? Enter Its finite) value if its…

A: We have to check

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.