| an+1 = o then E a, diverge an if lim n = 1 Select one: True O False 8.

Q: 1. If f(r) = , do the following: %3D iii) What is lim

A: Given Function, f(x)=1x

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: Evaluate the limit lim (tan x)cot O 1 O 5 5 None of the above

A: Given is      L= limx→π-2     tan xcotx      ∞0  indeterminant form  limit       taking both…

Q: Let n be a positive integer. For which n are the two infinite one-sided limits limx→0±1/xn^n equal?

A:

Q: Which of the following is equal to the limit limx→0 sin^2 2x/xtanx A.  0  B.  4  C.  2  D.  8

A: We have to find the limit Use l'hopitals rule to obtain the limit. Keep on differentiating the…

Q: S* 16sin(t")dt Evaluate the limit lim

A:

Q: 5. If b > 0, prove that lim = 0. %3D 1+nb

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

Q: A. Čalculate each of the following limits, c explain why it does not converge. You ma any theorems…

A: In the given question, the concept of limit is applied. Limit The limit formula is employed to…

Q: 2. b. lim a Csinza +cosa sin29) のッb ト Co」?a

A: find limit

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: Which one of the following is equal to lim 2 sec x – 2cos x :? The limit does not exist. a. О. 0.5…

A:

Q: Evaluate the limits: lim (cosx)cor*x 13. Ans: e12

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

Q: The limit exists and is equal to 0. Select one: O True O False lim (x,y) →(0,0) 36x²+25y² 6x+5y

A:

Q: Show: ( (|fl2 – €)² < lim sup E If (n) < (I|fl2 + e)² , Where ƒ E C(R | Z; , c) n=-N

A:

Q: lim,(1+ 1 = e

A: To prove the given limit

Q: Find following limit. lim (Va2 + 4x – Va? – 5x) a) 9/2 O b) Does not exist c) 2/1 d) 2/9 e) 0 O f)…

A:

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: Find the limit. ey?, P-(5, 0, -5) lim -1 sin O 1 TT оо

A:

Q: S* 56sin(t")dt Evaluate the limit lim .8

A:

Q: 3 (b) lim (sin r) In x I 0+

A: We have to find limit

Q: 4. Use the sandwich theorem to find the following limits: sin x (a) lim cos x (b) lim

A: a) -1≤sin x≤1⇒-1x≤sin xx≤1x⇒limx→∞-1x≤limx→∞sin xx≤limx→∞1x⇒0≤limx→∞sin xx≤0⇒limx→∞sin xx=0(using…

Q: 2sin?y 4) lim y→180° 1-cosy

A: Apply the limits and evaluate

Q: Show that the following: If r > 1, then lim Vr – 1 = 0.

A:

Q: Find the limit (e ut+t g +tan(6t)k) lim -4to it- Sin2t)

A: We have to find the limit.

Q: Find the value of the following limits: 5y 1-limy→0 tan 10y

A:

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

A:

Q: The limit lim (x,y) →(-2,-5) exists and is equal to -20. Select one: O True O False 25x²-4y² 5x-2y

A: The objective of the question is determine the limit existing.

Q: Prove the following. (b) lim( Vn² +1 – n ") = 0 - (c) lim Vn? n) = } 1 2 ||

A: Prove the following limits

Q: 2. Let r > 1. Prove that lim r" = 00,

A:

Q: Q2/Find the limiting values: lim Tan (4%) 必→。 O lim 7 7- x2

A: Explanation of the solution is given below...

Q: (b). Compute each of the following limits. (i). lim,4 ". (ii). lim,0 tanz

A: For (i),     limx→ 4x2-x-12x2-4x=limx→ 4(x+3)(x-4)x(x-4)=limx→ 4x+3xPlug in the value x=4.=4+34=74

Q: Find a o that works for ɛ = 0.01 for the following limit. lim 5z - 8 = 12

A: Given that: ∈=0.01limx→25x2-8=12

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

A:

Q: Show that when T(z) = az+b cz+d where (ad - bc ‡ 0), find lim T(z) = ∞ if c = 0. 7-3

A:

Q: Compute the following limits if they exist. 2 - VE (a) lim 244 3 - V2x + 1 (b) lim r sin

A:

Q: gives What is the value of a, such that after direct substitution the limit lim (x)1+Inx Select one:…

A: Given: limx→∞xa1+lnx=∞0 Use limit rule: if limx→af(x)=b and limx→ag(x)=c then limx→af(x)g(x)=bc

Q: Which of the following limits requires L'Hopitaľs Rule to evaluate? O A. x-2 lim 2x -2 O B. lim e…

A: According to L'Hospital Rule

Q: Evaluate the limit. lim (sin(4t)i + cos(5t)j + tan(2t)k)

A:

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: Find the limit. 10x? lim cos

A: Solution is provided below

Q: The limit: does not exist Select one: O True O False x² - y² lim (z,y) (0,0) 4x + 4y

A:

Q: tan z lim is Select one: a. e b. 0 с. 1 d. -1

A: Given limx→01xtan(x)

Q: Use continuity to evaluate lim sin(2x + sin 3x) Enter I for o, -I for –o, and DNE if the limit does…

A:

Q: ind the following limit. x2 + 1 lim (x, y) - (0, 15) arctan + (y – 15)2,

A:

Q: ven that lim f(z) = 1 and lim g(z) = -4, evaluate the following. lim (-4f(z) – 2g(x)) z-1

A:

Q: S 56sin(t)dt Evaluate the limit lim

A: Evaluate the limit limx→0 ∫0x56sint6dtx7

Q: To apply the divergence test for Σ „5/4n² n=1 we need to evaluate lim eS/4n?. n→∞ What is the value…

A: Here we have to find the value of the limit.

Q: s(2) is continuos if lim f(z) =f(z,)

A:

Q: O Evaluate the lim x sin (-), (Use Squeeze Theorem) 1-0

A: Given : The limit is limx→0 x sin 1x .

Q: - Evaluate the following limit 2 sin z – sin 2r a. lim

A: Evaluate the limit limx→02sinx-sin2xx3

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.