Prove that if r >1 then f r" dx converges to 1

Q: Q2 Prove that the scries 2+ x2 3+X2 4+x is Unitormly convergem? in any interval?

A: The given series is: 11+x2+12+x2+13+x2+……. Therefore the given series can be written as:…

Q: Suppose that |f(r)|I b where and g(r)dx converges. Prove |f(x)dr converges. that

A:

Q: Let f and g be as in the figure, we may deduce that if I g(x)dx converges then

A:

Q: 1 (a) Use the Integral Test to show that > converges. 2. n' +1 d 1 n = 0 -1 tan dx Hint: 1+x?

A: As per our guidelines, we are supposed to solve only one question.  Kindly post other questions  as…

Q: Let f and g be as in the figure, we may deduce that if | g(x)dx converges then f(x)dx |4 y = g(x) v…

A: We will use the fact that the definite integral gives the area under the curve. And then we will use…

Q: Consider the sequence of functions {fn}=2 where fn: [a, b] → R defined for n 2 2 by if 0<x s -n² (x…

A: Definition: Suppose fn is a sequence of functions fn:S→ℝ and f:S→ℝ. Then fn→f pointwise on S if…

Q: 2.66 Let fn(x) = z for all r E R. a) Find the pointwise limit of fn. b) Does f converge uniformly on…

A: Convergence and uniform convergence of the sequence

Q: 5. Let {fn} be a sequence of measurable functions on E = [0, 1] satisfying Prove that the sequence…

A: Recall.   1: Triangle inequality for integrals.   2: if (a_n)^2 goes to 0 as n goes to infinity then…

Q: Let fn (x) uniformly converge to f(x) on [a, b]. If fn(x) E R[a, b], then f(x) E R[a, b] True False

A:

Q: 10 Detemine whether the improper miegral lo F+16) dx diverges or converges. Evaluate the integral if…

A: Given the improper integral  I=∫0∞10x(x+16)dx

Q: Suppose fn : S → ℝ are functions that converge uniformly to f : S → ℝ. Suppose A ⊂ S.  Show that…

A: Suppose fn : S → ℝ are functions that converge uniformly to f : S → ℝ. Suppose A ⊂ S.  Show that the…

Q: 1.₂0 +00 1 2. Determine whether the integral da converges or rvin x diverges. If it converges,…

A: We have to find out integral

Q: 3.3 Prove that does not converge uniformly on R. k! k=0

A:

Q: Let f and g be as in the figure, we may deduce that if | g(x)dx converges then | f(x)dx a a | 4 y =…

A: Given two functions f(x) and g(x) It can be clearly seen that the area bounded by the function g(x)…

Q: Suppose that the sequence of functions {fn} and the function f are integrable on [a, b] and that…

A: Given that,  The functions fn and f are integrable on a,b. fn converges to f on uniformly a,b. an…

Q: Prove: if 0 is less than or equal to r which is less than or equal to 1, then (r^n) converges.…

A:

Q: ounded funclions on A to h,t converges uniformly

A:

Q: z . Prove that fn (z) = sin is uniformly convergent to 0 on D(0,2).

A:

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: Determine whether the improper integral x²e=x*dx converges and, if so, evaluate it. 8.

A: ∫-∞+∞x2e-x3dx

Q: b)does the integral converge 2x-2 dar (r+1)(x²+1

A: Consider the given integral. I=∫1∞2x-2x+1x2+1dx Now, find the partial fraction of the function.…

Q: Let r be a constant. Suppose >,r i=1 converges to 8, then the sum of >r' is i=0 Answer:

A:

Q: Let fn(x) = x¹(1-x), r [0, 1] and n € N. Show that fn = 0 on [0, 1] but that {f} is not uniformly…

A: Given fn(x) =xn(1-x),             x∈[0,1] and n∈N To prove: {f'n} is not uniformly convergent.

Q: If 2 a, converges, then la,| diverges. n=1 n=1 True False

A: Given statement is FALSE. I HAVE given a counter -example.

Q: 13.D. Show that, if we define fn on R by fa (x) 1+ n?x? then (fn) converges on R.

A: givenfn(x)=nx1+n2x2dividing numerator and denominator by x2fn(x)=nxx21+n2x2x2

Q: a) Show by example that E( an /b.) may diverge even thagh E an and E bn converge and no b, equals 0.

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: Let (fn) be a sequence of functions that are integrable on [a, b] and that converge uniformly on [a,…

A:

Q: Compute the point-wise limit of (fn) and determine if they converge uniformly on given intervals. 1.…

A:

Q: 5. Let h, : [0, o∞) → R be given by h„(x) and let h : [0, ∞) → R be given by I +n %3D h(x) = = x.…

A: Answer

Q: a] If the function f(x) is continuous in a closed interval [a,b] and f(a)f(b)<0, Prove that the…

A: let us prove the first part by considering a function let fx=x, x not equal to zero  and f0=1 but as…

Q: Prove that if a sequence of continuous functions fn :R→R is uniformly convergent on Q, then it is…

A: Given function fn:ℝ→ℝ sequence of continuous function. fn is uniformly convergent on ℚ To prove: fn…

Q: determine the domain AND the function to converge the serie e converge la serie: E=0 Re(u). n%3D0

A: Consider the given series

Q: Let fn(x) = nxe-n, for x = [0, 1]. (a) Show that for each x € [0, 1] we have fn(x) converges to 0.…

A:

Q: If (am) is increasing and en (an) is bounded by M converges to a, {|a1\, |a|}. max

A: Let (an) is increasing sequence and converges to a,

Q: Use mathematical induction to verify that the following integral converges for any positive integer…

A: An integral is said to be convergent if the integral has finite value that is the value of the…

Q: 1 Given f : [2, 0) → R, Prove that fn(x) = converges uniformly to f(x) = 0. 1+ x"

A:

Q: There is no value of r such that Jo (3t)-r 5 dt converges. 14.

A:

Q: 3. Let {fn}n=1 and {gn}-1 converges uniformly on E. Prove that {fn - In}n=1 converge uniformly on E.

A:

Q: Suppose that a sequence of differentiable functions {fn} converges pointwise to a function f on an…

A:

Q: Determine the convergence of the integral tan x d.x. E (In(cos r))2

A:

Q: uniformly co

A: Given, if fn and gn are uniformly convergent sequences of functions. To prove that fn+gn converges…

Q: Given f: [2, )IR, prove that fn (x) = けx" It, converger uni formly to f6)-o.

A:

Q: Show that if f(x) is integrable on every interval of real numbers, and if a and b are real numbers…

A:

Q: Determine the values of p for which f(x)da converges where f(x) = = 1-e-z TP

A: Here, in the question for what value of p the integral is convergent. The simple improper integral…

Q: Σ-(, n=1 n7/2 Put 'C' below if the integral converges, or 'D' if it diverges.

A:

Q: b) Prove that sin z is unbounded in {z E C: |Re z|< 1}. c) Prove that sin- is uniformly convergent…

A: We have to solve given questions.

Q: Consider the sequence of functions {fn}n=2 where fn: [a, b] → R defined for n > 2 by if 0 sxs fa =…

A:

Q: O Find the set s on w/c In )= x"(1-x") converges pointwise.

A:

Q: Suppose that fn(x) and f(x) are functions R –→ R. Suppose also that fn converges uniformly to f as n…

A: Suppose that fnx and fx are functions from ℝ to ℝ such that fn converges uniformly to f as n→∞.  To…