An = sin n = 1,2, 3, 4, . Find lim sup an lim inf an.

Q: (c) lim sup (an + bn) lim inf an + lim inf bn

A:

Q: Show that 1 lim 00 cos 0

A:

Q: 3. Let f(2) = if z + 2i, while f(2i) = 3+4i, is f(2) continuous at z = 2i? 2- 2i 4. Evaluate lim (az…

A: 3)Given:

Q: 1) a)lim n(a (aa – 1) =?

A: Given: limn→∞na1n-1 We can write, limn→∞na1n-1=limn→∞ a1n-11n We get the indeterminate form

Q: If lim [sin(zn)] In z 4 for n > 0, find the value of |3D n. In 4 In 2 4 1

A: Take ln both side and use l hospital rule

Q: 3 lim In cosy COS

A: Let,f(x)=limy→0y3lncosyput y=0,Therefore,=03lncos0=00 form,Therefore,using L-hospital…

Q: To compute lim,_30+ (sinx) (In x), first re-write in which form? sin æ A. lim,0* īn z In a B. lim,0'…

A: Given that: 1. f'' at critical points.2. limx→0+(sinx)(ln x)

Q: Let k be a positive number. It can be shown that lim be kb = 0. Use this fact to compute o*xe¯k* dx.…

A: Given, limb→∞be-kb=0        ......1 now compute ∫0∞xe-kxdx Apply integration by parts on given…

Q: 1 o. = 0. Show that lim x² sin -| *

A: Use the property that -1≤siny≤1. Take y=1x, then -1≤sin1x≤1

Q: n+1 Evaluate lim cos (x² )dr (and show all work)

A:

Q: Find the limits 1 lim el/ cos

A: We have to find the limit: limx→∞e1xcos 1x We know that 1∞=0

Q: n: (1) lim sin(1/n") 1/ns n+00 (2) lim 21 etin

A: 1. if limx→0sinxx=1limn→+∞sin1n81n8=1

Q: In x is I0 cot x lim Select one: a. b. -1 С. О d. 1

A:

Q: Find the limit. cos(70) - 1 sin(30) lim

A:

Q: Prove that lim x cos - = 7 %3D 1= 0.

A:

Q: Suppose In(A") lim In(tan z) -)- 1. Find the value M for cot 2r which A eM In(tan z) Türkçe: In(A")…

A:

Q: 2 Prove that lim x*cos 0.

A: Explanation: Given that,  limx→0x4cos2x=0     Taking LHS(Left Hand Side) limx→0x4cos2x

Q: Compute sin ax lim z0 sin bæ

A: L’Hospital’s Rule : Suppose limx→af(x)g(x) = 00  or  limx→af(x)g(x) = ±∞±∞ where a can be any real…

Q: -3k sin() - cos(;)| for k = 1, 2, ... and let A = lim y00 A(k). Then Let A(k) Select one:

A: We have defined a sequence of matrix as  A(k) =  - 3kSin(1/k) - Cos(1/k) e^( -1/k2 )  e^( -k2 )…

Q: Using the Sandwich theorem, what is the value of lim,[3 -2 cos(: n+1

A:

Q: Express the limits as definite integrals.

A: Given limp→0    ∑k=1n1ck∆xk

Q: B: prove that lim cos0 = 1 ||

A: We have to prove that

Q: So sin() -=? lim, o

A: Given that:limx→0+∫0xsin(t2)dtx3

Q: In(tan z) Suppose In(A³) lim -) – 1. Find the value M for which A = eM. cot 2z

A: Limit.

Q: If(z)- 니 < e. By definition Show that: lim, »1+i = - а. b. 4 lim = 2i. %3D 2- 1-i z2

A:

Q: tan s lim is Evaluate

A: On directly substituting the limit we obtain indeterminate form 00, so first we need to simplify the…

Q: In evaluating 2 dx 5₂₁²= is same as evaluating lim_cos-¹(f(x))|c. Determine the value of f(x) if…

A: Derivative of cos(x) = - sin(x) We have to find the value of f(x) at x=0.96

Q: Evaluate lim tan z sin z

A:

Q: 2.6 Show that if J sin ! if 0 < x <1, if x = 0, f(x) = then lim,-0+f(x) does not exist. (See Fig.…

A:

Q: The ratio test: {en =Tan+1/anl, p = %3D lim Po}. If p> 1 use a different test. True False

A: We will first state ratio test Then we will use the definition of ratio test to determine whether…

Q: Find the limnit. lim (cos(t), cos(t), tổ In(t))

A: Here we have to evaluate the limit.

Q: 5 sin(2z) z-40 1- cos(2) Find the limit. lim COS

A:

Q: Given the sequence an 1 [" 1 dx. Then find lim an-

A: an=1n∫1n1xdx, then find limn→∞an

Q: tan(2x) x+02sin²(x) Evaluate: lim O a. ∞ O b. -∞ O c.0 O d.-1

A: We have to evaluate limx→0- tan2x2sin2x         Here two sided limit does not exist.…

Q: 49. Let {x,}=1 be a sequence of real numbers such that xn Calculate lim,∞ exp(cos(x, – 1) – 1).…

A:

Q: Q 7) Find the limit or show that it does not exist. cos(r) In( -a) In(e- ea) sinx In (b) lim (a)…

A: Hey, since there are multiple subparts posted, we will answer first three subparts. If you want any…

Q: If A = [0, 2π] and A is measurable, prove that lim cos nx dx = lim [₁ sin nx dx = 0. n-∞ JA

A: Given that if A⊂0,2π and A is measurable, the objective is to prove that limn→∞ ∫A cos nx dx =…

Q: lim cos nл| 2n-1 - 2n+2

A: Use : cos x =1-x22!+x44! + ...........

Q: 39. Prove that lim x"cos

A:

Q: E. Show that if lim,-co an = 0, then O(a, 1) = O(1). %3D

A: given that  Limn→∞ an=0 now we find that Limn→∞-(an+1)

Q: answer about the following questions brainly. limx-0 sinx(1-cox) 2x

A: To evaluate: limx→0sinx(1-cosx)2x2 Solution: limx→0sinx(1-cosx)2x2 On simplifying further we get:…

Q: Find the value of lim ((n + 1) cos (n + 1) cos¯¹ (1) − n) n

A: Given: limn→∞2πn+1cos-11n-n To find: The value of given limit.

Q: 4. If an + 0, prove that |an+1| lim inf |an+1| < lim inf Jan| < lim sup lan] <_lim sup |anl |anl…

A: The given question is related with real analysis. Given that , an ≠ 0 . We have to prove that…

Q: Show that the limit If cos( 1/ y)<3 the find the limit lim (x, y) (0, 0) 4 x cos( 1/ y)

A: We are given that cos1y≤3.  We need to find the limit, limx,y→0,04x cos1y.  Taking the absolute…

Q: 4. Evaluate lim (cos r)/**.

A: We know that limx→0f(x)g(x) is of the form 1∞ then limx→0f(x)g(x)=limx→0eg(x)f(x)-1

Q: Use e-ð to prove lim,1 sin x = sin 1. [Hint: we know sin(1 +h) = sin(1) cos(h) + cos(1) sin(h),…

A: We have to prove: limx→1sin(x)=sin1

Q: (a) Show that lim | x| cos = 0.

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…