a. Assuming that lim,(1/n') = 0 if c is any positive con- stant, show that In n lim n° п—00 if c is any positive constant. b. Prove that lim,(1/n°) = 0 if c is any positive constant. (Hint: If ɛ = 0.001 and c = 0.04, how large should N be to ensure that | 1/n – 0| < ɛ if n > N?)

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:

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A:

Q: 2.2 a) Prove that lim,-2(x +2x – 7) = 1 using the e- ô definition of a limit. b) Find lim,-2 arccos…

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A: The given symbol is the symbol of the limit of the function at the given point of limit.…

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A:

Q: Let A.=(-11.1- and B. 4. for all n E N. 1. PL lim PL(A) 2 BUB. =2 3. AL lim u(A.) -3.

A:

Q: H.w iF FX)= *+b x<I and Lim F(X) 8,F(-1)=2 Find asb and when X#0

A: Solution:

Q: Recall that the Power Law states that for any positive integer n, lim [f(x)]" = ( li Apply the Power…

A: Topic  =Limits

Q: & Prove that lim I = 2 using the e-d-definition. Hint: Vr %3D

A: Given: To explain the given statement as follows, Here, prove that limx→4 x = 2.

Q: 1- Find the direction of the vector with initial point P(-3,4,1) and terminal point Q(-5,2,2).

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

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

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Q: Find lim (a + 2ar + 3ar² + n→∞ .. +nar"-¹) where |r|< 1.

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Q: (1+*)"- TL limn TL O a. V2 O b. 00 O c. 1 O d.e v2 O e. does not exist O f. V2 9. ev2 Ch. 0

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Q: 3. Let f(x) = x and P = {0, nn = 1}. ... + f("1) and that lim Lf(P) + k = k(k +1)/2) 1 Show that…

A: Given the function f(x) = x &amp; a partition of the interval 0,1 as P =0,1n,2n,3n,...nn=1. First we…

Q: az? + sin y f(x, y) = and let L = lim(z,p) >(0,0) f(x, y). Which 29z² + y? of the following…

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Q: Find lim 1-CoS 3X Xう。 tan x -1 lim メー X - X->

A: Solution is given below..

Q: 7. Find each limit. . a) lim (2x +Vx² +5 7a. x-0 6x – cosx b) lim- x-* x+sin 3.x 7b. 2x c) lim 7c.…

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Q: Show that if xn ≥ 0 for all n € N and lim(x₂) = 0, then lim(√//xn) = = 0.

A: To prove:-If  for all  and  then

Q: Let a > 0 be a real number. Prove that lim x“ sin = 0.

A: