rove that then if Ean converges Lim(ant antit t antr) =0,r20 ハ→ 0 O Does imply that Ean Converges? Give reason for youn answer.

Q: •1 2. In r dr

A:

Q: Find the Value of p which intagral the Converges, abso leste ly Cosn du- Conditionaly. to Jean de

A: Comment: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Determine whether the following impoper integral converges or diverges: (Hints: First use…

A:

Q: Let f : A → R and (x„) ,(yn) are two sequences converges to c such that Xn, Yn # c, Vn E N. If…

A:

Q: (x--1)dx Vx6-64

A: Given integral  ∫2∞ x2-1x6-64 dx

Q: + R be defined by fn(x) = an Find the pointwise limit in 1.3 converges uniformly on [–3, 3]?…

A:

Q: I need To find a Sequence of functions (m c^(E-!, 13) That is cavchy Cuith Il ) and does not…

A: Given: C1-1, 1 To find: A sequence of functions in C1-1, 1 which is Cauchy but not convergent in…

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

A:

Q: 18 For which numbers a does x,+, = a{x,– x) converge to x* = (a – 1)/a?

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: Are there value of fer which omy ĭ he converges.

A: A  series is said to be convergent if ad only if the sequence of partial sums of the series…

Q: Decide whether the following proposition is true or false. Provide a justification for your answer:…

A:

Q: (j) F= R, V = {vER: Un converges as n → ∞0}; (k) F= R, V = {v ER: un converges absolutely as n→ ∞0};…

A:

Q: nd is it or diver Convergent (0.627 an %3D (3.15)"

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Show that if a>-1 and b>a+1 , then the followingintegral is convergent.

A:

Q: MEDI is a) converges to 2 b) converges to 2/2 c) converges to 23 d) diverges e) None of all

A:

Q: The following improper ategral(r- De **!dx converges to3e convergesO optich

A:

Q: A): Let Using only the defination of xate of chamge in tems of limit, Compute dy the defination of…

A:

Q: Determine whether or not the infinite series below converges.

A:

Q: Use the root test to determine whether ye converges, where An is as follows. an =

A: Explanation of the answer is as follows

Q: Determine whether the seauence converges ordiverges. If it coveges, find the loo+n00+Cnn) o n! + Sn…

A:

Q: determine whether the doubly infinite improper integral converges and, if so, evaluate it.Use…

A:

Q: 4 xP x9-

A: We will find the value of intergral. If the value is finite then this improper integral would be…

Q: Determine i it convergcs or dverges. Evaloate if converges oo dv 2.

A: We have given,

Q: Exomples Porfrm 2 Thera trons of a a convergent fixed pornt methad to approximate the root of the…

A:

Q: The improper integral 2e*dx is: (a)converge to 2 (b) converge to – 2 (c) converge to 0 (d) diverge

A: To solve the given improper integral.

Q: Use the root test to determine whether . converges, where an is as follows. (1 + Ink)*

A:

Q: thi Prove that the improper integral } ] docdy (1 + x² + y²) ³¹²/₂ Converges

A:

Q: If lim,- f(x)=0, then f(x)dx converges Select one: True O False

A: As the mention in above given question when x goes towards infinte than function f(x) gives 0. It…

Q: Use the Ratio Test to prove convergence or divergence: 2n+2 (n+2! (n+2). n=1

A:

Q: dx Determine if the improper interal S, xc Fnd it valne if it converges. Conneeges on diree jes.…

A:

Q: Use the comparison or the limit test to find if the integral converges or not.

A: ∫394x-16x2-9 ·lnx-3dx

Q: determine if The fenes Converget, E Converges, fınd The fum it

A:

Q: d the radius of convergence of p(z) =E (z – 1)2". Hint: It is not 2.

A:

Q: Let 1 = S dx c+∞ 4-x I = dx Then I O converges to 3 O converges to .

A: Consider the integral: I=∫1+∞4-xx3dx

Q: 1By the monotone converges Theorem, snow that nis siquence convergus 2.4 .. (2n) ** 3.5 --- (2nt1)…

A: Given : The given sequence unn=1∞  is defined as,    un = 2.4.6 ....2n3.5.7....2n+1  ;  n≥1 To prove…

Q: Use the Integral Test to determine if the serie 1 Σ (n+ 2)°/¾ n=1 converges or diverges.

A:

Q: petermine if the improper integral ex J dx is convergert or diverg unt. If it is convergent,…

A:

Q: 2. For each of the integrals below if convergent evaluate the integral, otherwise show that it is…

A: Given: the integral below if convergent evaluate the integral, otherwise show that it is divergent.

Q: Let f : A → R and (xn),(Yn) are two sequences converges to c such that Xn, Yn # c, Vn E N. If…

A: We understand this statment by the help of an counterexample .

Q: Set an where r E R is a real number. Prove that ɑn converges to 0 if (-1, 1), cônverges tó 1 if r =…

A:

Q: Show by example that E(a,/b,) may converge to something other than A /B even when A = equals 0. Σαν…

A:

Q: Show that if (sn,tn) converges to (s,t) in ℝ2 with the usual d2 metric, then the sequence converges…

A:

Q: The set S on wc fn Cx) = 1+ x" Converges pointwire ?

A:

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

A:

Q: Suppose that f e C(R) and that | If(x)|dx converges. Show then that 2 f(x)| sin nx|dx sx)dx. lim n00

A:

Q: 1 n³ + nªx²

A:

Q: {au, ) IL x y² dx dy Q4-A) Show that the sequence B) Evaluate : ah (sinn)}, +sinh( converges to (1).

A: Given

Q: Perform a testto determine if. S a J y converges diverges or

A: