00 Let a, = 1- /1 -. Show that lim an = 0 and that > an diverges. Hint: Show that a, > 2n n=1

Q: B. Prove the fillang tim Jn2 +n 4- (6) lim n-700 Lvntl trn

A:

Q: In(x – a) For a e R, which statements do hold for the one-sided limit lim ? 1¬a+ In(e² – eª)

A: Here we use L'hopital's rule

Q: If lim an 0o and En1 a, diverges, then E b, diverges O True O False

A: taking the an and bn such that the given statement is False...

Q: lim ("V52"-1 52n-1

A: F

Q: 42. Prove that if lim "O = 5, then lim h(t) = 15.

A: It is given that To prove that

Q: Suppose lim, An = 1. Prove that 1 lim E(-1)*a2k = 0. n-00 n k=1

A: Given that limn→∞an=1. To prove limn→∞1n∑k=1n-1ka2k=0.

Q: Note: You may need to assume the fact that  lim M→+∞ Mne−M = 0  for all n.Sales of the text Calculus…

A: To calculate the total future sale of the text.

Q: Let f e C(0,1). Suppose that lim f(x)= lim f(x) =+∞. Show that f acheives its minimum in (0, 1).…

A: Given: f∈C0,1 limx→0+fx=limx→1-fx=+∞

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

A: We will apply l-hospital rule as infinity/infinity doesn't exist

Q: Pick 8 of 10: Prove or provide a counterexample. lim Sn =0 if and only if lim s,=0

A:

Q: Express the function n, lim n→+∞ 4k² in closed for and then find the limit. n³

A: We will first write this function in closed form then we will calculate the limit of the function.

Q: S 20sin(t )dt Evaluate the limit lim

A: Given:         limx→0∫0x20sin(t3)dtx4

Q: lim 2+x) In(1-x) x0 (1-e*) cos x

A:

Q: Suppose a function f (x) has a vertical asymptote at x = a. Which of the following conclusions are…

A: The objective is to find which of the above conclusions are guaranteed.

Q: a) lim 2x e* +In x = ?

A: To find: The value of limit limx→+∞e3x+ln xe2x+x2. Concept used: Properties of limit:…

Q: Determine whether the following statement is true or false. If this statement is true, explain why.…

A: If limn→∞an=πthen an must be conversent. Reason- an is the fuction of n and when n is tending to…

Q: in Q5. Find the value of the limit: lim in — е 2 2+1 Z→e 2

A:

Q: Suppose that a, > 0 and converges. lim na, = 0. Prove that Ea, n 00

A:

Q: 1. Show using sequences of functions that lim -nz? e dx 0.

A: Solution is below

Q: бп? + Зп = 3 2n2 – 5 Prove lim 6.

A: Limit of the fractional  value

Q: Show that if lim(a /n) = L, where L > 0, then lim(a,) = +0o.

A: Consider the given information: limn→∞an/n=L,  L>0 To show that limn→∞an=+∞.

Q: 4x In z (a) Evaluate lim エ→1( (1- 2)-- -1) C.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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

A: Substituting x = (pi/2 - h) & using L- Hospital rule

Q: Use the definition of limits (ε-N) to show limn→∞ ((n/(2n−1)) = (1/2).

A: Find the subtraction value of sequence and limit

Q: Suppose that a, > 0 and lim a, = ∞. Prove that Sa, diverges.

A:

Q: Calculate the following limits, or explain why they diverge. Зn? + п — 1 lim n0 -2n2 +n – 4 x² – 9…

A:

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

A: Limit.

Q: The limit lim (x c 1 X• COS is an indeterminate form of type 0· o. Select one: True O False

A: Given: limx→∞x·cos1x   As we know that; limx→afx·gx=limx→afx·limx→agx

Q: If lim, +00 an 0 or lim,,00 a, does not exist, then an diverges. Select one: O True O False

A:

Q: Q. Prove that: Lim tanhx =1 .

A:

Q: Calculate: lim n =1 as follows: n = n% Innh Calculate lim In n and use this to determine lim Vn. = e

A:

Q: 9.6. Find the limit lim,0+ [Log(a + iy) – Log(a – iy)] when a > 0, and when a < 0. -

A: To find the below limit. limy→0+loga+iy−loga−iy

Q: Let an 2n+4n-3 Using the definition of the limit, prove that lim,∞ an 3n2+2n+1* 2/3.

A: Given that, the rational function  an = 2n2+4n-33n2+2n+1 To prove that limit of function is limn→∞…

Q: Evaluate The limil lim at4 X-4 (a) 1 ® Indefinite © er O d a >>

A: We have to find the required limit for the given function.

Q: Evaluat the limit si a. lim (Itx)"-1-nx ー1-nx x2 メ

A:

Q: In (2r) Find the limit: lim

A:

Q: e -e lim is z0 In(1+ 2x)

A: Given limit:

Q: Suppose In(A5) In(tan z lim ( 1z))- 1Find the value M for cot 2z which A = eM

A: Here given as lnA5=limx→π2-lntanxcot 2x-15lnA=limx→π2-lntanxcot 2x-limx→π2-1

Q: Compute the limit 1 e¯nt lim dt. VE n-00

A: Given: limn→∞∫01e-nttdt

Q: 3 (c) Apply the monotone convergence theorem to evaluate Lim fn(x)dµ.

A:

Q: .t 5-1 lim t t → 0

A: By L' hospital rule we solve above limit.

Q: %3D In(1+x) 3.A) lim P-ove tha t マー0

A:

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

A: lnA3=limx→π2-lntanxcot2x-1 We have to find value of M such that A=eM

Q: 1 Q5. Use the precise definition (i.e., via the e 8 notation), prove lim х-2- (х-2)3 = -0.

A:

Q: → レしし Q2: Let c E R and let f be defined for x E (c, ) and f (x) > 0 for all x E (c, co) Show that…

A:

Q: 3. Prove the following using the epsilon-delta definition of a lir a. lim (2x – 1) = 3 x→2

A: We will prove the limit using definition.

Q: Exercise 3 Prove that t2 lim (1+ (19)

A: The given expression is in the form of one to the power infinity. Let L=limp→∞1+t2pp+12. In the…

Q: Using e – N description to prove that lim = 2. n2 +1

A:

Q: 7. Suppose lim nan = A +0 where an is not necessarily nonnegative. Prove >a,n diverges. n=1

A: