The sequence a, = sin (A) is unbounded (C) converges to a number less than 1 (E) diverges to infinity (B) is monotonic (D) is bounded

Q: The sequence (tanh n) converges to2 Select one: True O False

A: To find the convergence of sequence

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: Consider the sequence {fn(x)}, where sin(nx) fn(x) = 1+ nx Use the uniform norm to show that the…

A: Given: fn(x)=sinnx1+nx To show: fn(x) is uniformly converge on [1, ∞).

Q: 3. Define fn on (0, 1) by fn(x) = x". Show that fn converges to the constant function 0, but that…

A:

Q: How would I find if the sequences an=nπ cos(nπ) and an= (n2)(1/n) are convergent/divergent?

A: To examine the given sequence regarding convergence, that is study the limits as n tends to infinity

Q: Determine whether the sequence xn =√(5+3n+7n2)/(4n2-n+2), converges or diverges. If it converges,…

A:

Q: If 2 a, is convergent with positive terms n=1 is it true that sin (a,) is also n=1 convergent?…

A:

Q: Find the interval of convergence of Σ 6" (2n + 1)!

A:

Q: Ρτοve that the Sequence Converges and find i ts limit.

A:

Q: if Xn is bounded, is Xn  cauchy ?  is Xn convergent?

A: Solution

Q: de -- e* + 4e* -00

A: Given

Q: 4. Show that the sequence {fn}, where fn(x) = xER 1+n°x2 is point-wise convergent but is not…

A:

Q: Find sequences (xn) and (yn) so that xn - Yn 0 and yet does not converge to 1 Yn

A: By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: 1 n4 + sin“ n=1

A: To find that the given deries diverges or converges

Q: Find the interval and radius of convergence. (Зх — 4)" (-1)" (2n + 1) n=0

A:

Q: cos NII N 2) Show that converges/diverges.

A:

Q: Show that the sequence f.(x)} converges to a limit function (that you should determine) for each XEI…

A:

Q: 3. Prove that the sequence sin(n) (0, 1). converges to n n+1

A: We calculate both limit separately as n tends to infinity.

Q: We can show that the series 1 2" – n n=1 Σ is convergent by applying the limit comparison test with…

A:

Q: Find the interval of convergence of ) n°x" and find its sum. n=1

A:

Q: Use series to evaluate the limits

A: Given: limx→0ex-e-xx we know that…

Q: х Zn=0 п! x2n Ση-0

A:

Q: Show that the sequence of functions {f.} where f,(x)=: 1+ nx „xER is non-uniformly convergent on…

A: Show that the sequence of functions fn(x), where  fnx=x1+nx2,  x∈ℝ is non-uniformly convergent on…

Q: 4. Show that the sequence {fn}, where fn(x) = xER 1+n°x*' is point-wise convergent but is not…

A:

Q: 4. Show that the sequence {fn}, where nx fn(x) = xER 1+n°x is point-wise convergent but is not…

A:

Q: A sequence of functions that converges pointwise on [0, ∞0) but does not converge uniformly [0, 0).…

A:

Q: Find the radius and interval of convergence for (-1)"(x – 1)" n4" n=1

A:

Q: Find the exact value that the sequence sin" 1 converges to. (Note that as usual, sin" x means (sin…

A:

Q: Find the limit of the sequence if it converges; otherwise indicate divergence. tan-1 n 1) an

A:

Q: The radius of convergence (2n + 3)! (x- 1)" is | None of these infinity

A: Given ∑n=0∞(2n+3)! (x-1)n Compare it with ∑n=0∞ an(x-x0)n Then an = (2n+3)!an+1 = (2(n+1)+3)! =…

Q: Determine if the sequence an sin (20n) converges or diverges. If it converges, compute its limit. If…

A:

Q: 2. Use the definition to prove that if (xn) is a sequence of real numbers which converges to -3,…

A:

Q: The sequence {x}=0, where xn 20" is convergent.

A:

Q: Show that the sequence of functions {f.} where f,(x)=nxe is non-uniformly convergent on [0,1]. (by…

A: Test for uniform convergence of sequences: Let fn be a sequence of functions such that it converges…

Q: 2. Show that following sequence of functions are convergence pointwise to its limit function. a)…

A: See the attachment

Q: Find the exact value that the sequence sin" 1 converges to. (Note n=0 that as usual, sin" x means…

A:

Q: Find the radius of convergence for ∞∑n=1 (sin^2 (n))x^n

A:

Q: The interval of convergence of (-b)" x"*1 where b > 0; is n+1

A:

Q: Find the radius of convergence of (-1)"x' 4n n=0

A:

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

A:

Q: The sequence a,=n sin 1 converges Select one: True OFalse

A: We have to check

Q: Find the interval of convergence for the function (x-5)" g(x) = > Σ 3" Vn + 2 Make sure to check the…

A:

Q: 4. Show that the sequence { fn}, where nx fa(x) = xER 1+n°x2 is point-wise convergent but is not…

A:

Q: 4. Show that the sequence {fn}, where nx fn(x)=- xER 1+n°x' is point-wise convergent but is not…

A:

Q: Find the first 4 non-zero terms of (1+3x)^(1/4) centered at x=0. what is the radius of the…

A:

Q: Prove that the sequence {sin(nn/3)} does not converge.

A:

Q: Find the interval of convergence of Ln=1 (r-1)" 2n

A:

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.