The goal is to find lim So.nj(1 – * )"e-™*dx. - TX n-+00

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: Q: Prove that Lim %3D n-a

A:

Q: Find the limit: 5 cos(n) (8n-1)(n+10)) lim + n- 00 in 9n2+n+3 ||

A: on solving this we get the

Q: п+(-1)" (2n + 1) Sn

A:

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

A:

Q: 2+ 1 ** Evaluate lim - X+ oL dt A B none of these 1- e? 1 4

A: Given that,  Now taking the integral term,

Q: 3. Solve for -). the lim |t In(1 +

A: The given expression of the limit is: limt→∞tln1+3t

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: lim An lim PiAnl = PiA) %3D n-14

A: Given the sequence An and limn→∞An=A. We have to prove that limn→∞PAn=PA.

Q: (a) n+ (-1) 2n lim

A: limn→∞-1nn+12n

Q: (2) Show that Jo for a > 0 but not for a = 0. lim 818 √ne-na² da a lim √ne-na2 748 da

A: We have to show that,   limn→∞∫α∞ne-nx2dx = ∫α∞limn→∞ne-nx2dx  for α>0  but not for α=0.

Q: It is known that lim-0 eAt-0 for A What can you say about e? Justify.

A:

Q: 2. Prove that a. lim, b. lim,1

A:

Q: Show that lim (1 + = e. lim

A: To prove:

Q: 7 Find lim E n-00 k=1 n+7k

A:

Q: Find the limit: (1 -4)" lim n- 00 in

A: Here we have to find;  y=limn→∞1-2n3n

Q: 15.) Show that lim((2n)/"): 1/m =1.

A:

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: Show that 2n lim n+2 = 2,

A:

Q: Evaluate: lim, (cos z). Show your solution. O -1

A: Limit of a function f(x) at point x = a exists only when Left hand Limit(LHL) = Right hand limit…

Q: find the limit or explain why it does not exist

A: To find the limit.

Q: Show that lim Vn = 1. n-00

A:

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: Find the limit by L'Hospital's rule (whenever app 1 cos(x)-1+x a) lim- 2x4 b) lim

A: Explanation of the answer is as follows

Q: 17. If lim- X- 200 – 4n + kn² then k =

A: Given

Q: he limit (if it exists). (If an answer does not exist, enter DNE. Round your answer to four decimal…

A:

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

A:

Q: Identify the quotient as an indeterminate form of the type or tan(9x) lim x → 0 In(1 + x) Find the…

A: Using standard formulae of limits to solve this limit.

Q: Find the limit. 3 3. lim 3n n00

A:

Q: (7) ifa lim has a point that the equalio- prove PCz,y) is above L and only if 3x +2y >4

A:

Q: 7. Show all steps to find the lim sin (e-k) or show it diverges e-k

A:

Q: Evaluate 1- lim sırx

A:

Q: Prove that lim vn+1= 1. n-00

A:

Q: e) Finally, prove that lim az-2 does not exist.

A: Use left hand limit and right hand limit to proof it

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: Let m and n be two positive integers greater than 1. ecos (α"). am m then the value of (1) is n If…

A:

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: Show that lim (1 – 2²)"dr 0, n 00 0,

A: To show limn→∞∫01(1-x2)ndx=0 without attempting direct intergral.

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

A: Given limit:

Q: (b) From part (a), we know that lim an exists. Compute it. n00

A: Given that a1=3 and an+1=12+an for each n≥1 Also, the sequence an is monotonic increasing and…

Q: 1. Find lim,→0 k e'

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: Show that lim n2 +00

A:

Q: Find the limit. 2x2 3. lim Cos

A:

Q: A company training program determines that, on average, a new employee can produce  N( t) pieces of…

A:

Q: 3 In(z) Carefully define lim 21 2-I = 3, including phrases with e and d. %3D

A: Note that lnx&lt;=x-1  I have used that inequality to prove the statement

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

A:

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.