2n +1 a) Using the definition, show that lim n00 3n +4 3

Q: 2a Find lim a--I a -a - 2

A: To find:lima→-1-2a2a2-a-2

Q: ंनपह -4 Find the value of a such that lim 2-27-3

A:

Q: Find a number bER such that lim x²2x-3 C. %3D Solve the above question for cS

A: Given limx→bx2-2x-3x2-1=CTo Evaluate value of b  when C=5

Q: 6. Find lim Vn? +n–1 -). 2

A: n2+n - n = n2+n -n × n2+n +nn2+n +n = n2+n2-n2n2+n +n =n2+n-n2n2+n +n = nn2+n +n

Q: Prove rigorously that lim (4 + 8x) = -4. X-1

A:

Q: Find 23 + 8i (а) lim z-2i z2 + 4

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

Q: 22 — 62 — 6zі — 16 — 121 and - - Evaluate lim z→8+6i z2 – 8z – 6zi write it in the standard a +…

A: Please find attachment for the details solution

Q: 5. a) Explain why lim vx-3 does not exist. b) What about lim V(x 3)2 ?

A:

Q: Show that lim Z-2 (2-2)4 || ∞

A:

Q: n Find lim am. An 4 ||

A:

Q: 84. Prove that if lim ar = L, then lim ak11 = L. k00 %3D k00

A: limk→∞ak=L

Q: 1 Find all values of a, such that ]lim a exits and finite. (x-1 х*-1 x->I

A: limx→11x-1-ax2-1

Q: (b) With the help of Sandwich theorem (or Squeeze theorem), show that lim (2 √√x - 1)" = x² for x ≥…

A: By using Sandwich theorem,  we have to show that ;   limn→∞2xn-1n = x2  for x≥1

Q: The answer to lim (2 + e-) is Answer:

A:

Q: r - 1 lim 11 x" - 1 where n2 2 is an integer,

A:

Q: find lim (2 x3 - 3 x + 5) X --> -1 O 6 O none of these answers O 4

A:

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: What is lim x-inf (x_n) and y=lim sup (x_n) where x_n = [(-1)^{3n}] + 2?

A: We have to find the lim inf and lim sup of sequence

Q: Evaluate the limit 4 b lim b->4 2- V6

A:

Q: Investigate limθ→0sin nθ/θnumerically for several positive integer values of n. Then guess the value…

A:

Q: ■ Find the limit.

A: The given expression is limt→∞t-tt2t32+3t-5

Q: a) Using the definition, show that lim 0. 7n +8 n-00

A: Multiple questions are asked, I am answering the first question.

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

A: To find the limit.

Q: Using the ε − N definition of a limit, prove that lim(n→∞)=(6n^3 −2n+1)/(2n^3+1)=3.

A: In the given question we have to prove the following limit by using ε-N definition…

Q: 5. Is there a number a such that Зx? + ах + а + 3 lim x→-2 x? + x – 2 | exists? If so, find the…

A: Topic:- calculus

Q: Prove that lim 7xt3 = 10 wing epsilon delta proof.

A: Answer

Q: 85. Show that lim n! = 00. Hint: Verify that n! > (n/2)y"/2 by observing that half of the factors of…

A:

Q: Prove that lim x 2 = 4. x→ 2

A:

Q: limf is

A: Question 1: The answer is option first: 1 i.e. limx→-6 f=1 Question 2: The answer is option first: 2…

Q: 1. (f Use "e- N"-statement to prove that lim n 1 [Hint: Ve > 0,3N(e) = > 0, Vn > N, we have n- %3D

A: We have to show that given limit of function converge to 1-

Q: 6-2x Prove by definition that lim 4. 3

A:

Q: 5. Prove that lim Show your t→-2 t+2 complete solution.

A:

Q: Show that lim inf an <lim sup an. n00 n00

A:

Q: Using the ε − N definition of a limit, prove that  lim n→∞  (6n^3 −2n+1)/(2n^3 + 1) =3.

A: Given the limit function for provinglimn→∞6n3−2n+12n3+1=3

Q: . Determine the value of a such that lim I--2 3x² + ax + a +3 x²+x-2 exists. Justify your answer.

A: *By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: ii) Show that lim - 1+22+33 +...+n' "]=1 1/n

A: Apply Cauchy Frist theorem on limit

Q: 7. Find the limit. (Let c and d represent arbitrary real numbers. If an answer does not exist, enter…

A:

Q: 1. 1. 8-3 1 Evaluate lim 1 6-3r 9. Enter an exact answer. Provide your answer below:

A: SOLUTION-

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: applying lim 6-ydy can be eliminated by The infinity in the V6-ydy t-- 80 O True O False

A:

Q: 1² – 1 - 1 lim +1- a? – 2x +1'

A: To

Q: 37. Prove that lim x2 = 25

A: The given function is

Q: Evaluate the limit. 3i lim > N2 i=1 (Use symbolic notation and fractions where needed.) N 3i lim N2…

A:

Q: In formally proving that lim (x² + x) = 12, let e > 0 be arbitrary. Choose & = min т Determine the…

A:

Q: 4. Show the identity 1+ = (1+) (1+), then use it to prove n+1 (1+ 2) - = e?. lim n 00

A:

Q: Use ɛ - 8 def inition to prove lim x 8. %3D X2

A:

Q: 2. Prove that 3 lim 0. (HINT: This proof needs a ɛ-M type argument.

A: To prove that limx→∞3x=0

Q: m An = {-: m e N}, ne N, where N are non-negative integers. What is lim inf An and lim sup A,? n-00

A: The given set is An=mn: m∈ℕ, n∈ℕ

Q: /4+х — 2 - lim

A: