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Q: Consider the ceiling function [z] = min{z € Z]z >1}. This basically rounds up any real number. For…

A: To show that the limit doesnt exist the key idea is to show that the Left Hand side limit doesn't…

Q: 50. Calculate lim, sin(). (Proof is not required) n+2 n-+3

A: We have to calculate the limit limn→∞sinn+2n2+3

Q: If lim g(x) =15 and lim h(r) = 29 then lim [3g(z)- 7h(z)] エー-6 O 21.00 O 58.00 44.00 30.00 O-79.00…

A: Expand the expression and use the given limit values.

Q: 7. For what values of k does lim,→4 -+k exist? (a) – 2 (b) 4 (c) 1 (d) 8 (e) No such value exists.

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

Q: Ve 3n 2n an Find lim an n

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Q: 5x y Which among the following statements is true about lim(x.y)-(0.0) 3,8+2,2 wwwwwwnu None of…

A: We have to find the limit

Q: 1 lim x→-∞ ex Select the correct response: O +0 O 1

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Q: 6. Evaluate lim r/(1-z) 2+1+

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Q: Lim Vn' +n

A: Explanation of the answer is as follows

Q: Which of the following statement(s) is TRUE? 1. lim,0 = 1. x2 V1-x? II. lim,→1 does not exist. 2а —1…

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Q: 4. Evaluate: lim (a² + e-*)(= cac r) エー→0+

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Q: 3n+4 n+2 6. Let an Determine lim a, п+1 A) 0 В) 1 С) е D) e? 3 E) е

A: The solution is given as

Q: fn. (1,00) Evaluate lim

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Q: x + a Find the number a so that lim = 5. x + 3a Lütfen birini seçin: In 5 a. - 2 In 5 O b. 4. In 5 O…

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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.

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Q: 5. Let k(x) = + 3. %3D 2+e 5.1. What is limx→-ok(x)? 5.2. What is limx++k(x)?

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Q: Iff(x)= a,x". x"+....+a,x+a, - with a 0,b>0 b x"+..+b,x+b, m m Then show that limf(x)=oif n>m x→0

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Q: n |2n lim n→0 Vm²

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Q: 2. tanx カイ Lim (3, 주 so +1 wi7

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

Q: 24. lim xsin- is 110 (A) 0 in(s (B) ∞ (C) nonexistent (D) - 1 (E) 1

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Q: 48. If L = lim (cosec x)/(x, then the value of nL is - X->0* (A)1 (BY-1 (C) 0 (D) none of these

A: To evaluate: L=limx→0+ (cosec⁡x)1/ln⁡x Taking ln both sides, we will get ln L=lnlimx→0+…

Q: lim  2 t − 18 /5 t − 45 lim 9

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Q: 5x + 27 20 + 10x + 9 Evaluate lim O Undefine O 1 O 1/4 оз

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Q: s(x)= 4ex / 10x 2 What is lim s(x)?            x→+∞

A: Firstly, we will plug x=infand we get inf/inf

Q: f x^n / e^x =__

A: lim as x goes to infinity of x^n / e^x = 0

Q: 1x+ 7=3 7-4x 2. Evaluate lim,→∞( x2 4. ) exactly. S

A: To evaluate the below limit

Q: (e) 3. lim xsin

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Q: lim Un'tl-n):

A: Consider the limit limn→∞n2+1−n

Q: 1-e-* lim x→0+ 2x2 -00 00 O None of these 1 || O O O

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Q: e? – 1 – z lim 2 z-0

A: The given problem is: limz→0ez-1-zz2

Q: 1 n+2-(n- 1)+3 (n-2) +..+n 1 +2 +...+n° The value of lim is (a) 1 (b) (c) V2 (d) T-IN

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Q: If lim f(z) = 16 and lim g(z) = 25 then lim(3f(z)g(2)-71 = 1207 O 1200 O 1193 O 32 O 223

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Q: m,n >1 is -1 lim エ→1 T Select one: TL b. C.-T d.

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Q: Let x - for n - 1,2, 3, .... Then lim l equals O ve3 Oe-! Ove

A: we have to find the value.

Q: Q.1. Make a guess about the lim x-1 , when x= 2,1.5,1.1,1.01,1.001,1.0001,0, 0.5,0.9, 3 x->I x' -1…

A: Plug in the limit, 1 in x-1x3-1 and simplify to obtain that when x approaches to 1, the equation is…

Q: x-4 The lim,4 Va-2 does not exist. Select one: O True O False

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Q: for n > 1. Show that lim an exists and find the limit. 2 An 4. Let a1 = 1, аn+1 %3D n00

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Q: U EValuate 1he following a) lim メ→ x3 -1 - 1 メ+ b lim メう。

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

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Q: If lim f(z) = 13 and lim g(z) 22 then lim 2f(z)g(x) -7] = 579 O 565 O 572 O 26 O 180

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Q: a. lim,o ( 2 i +etj+4k) a. limț0

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 3. Use the graph of h in the figure to find the following values or state that they do not exist. а.…

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

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Q: xe" – In(1+ x) is lim x2 :Select one .a 4 .b 2 .C .d 3 3 一2

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Q: 3 Given f(x) = (4-a)3 Evaluate lim,-+4f(x)

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Q: (g) Let fG) be diffaentioble and lim fC) = 00 If lim :o then lim fGJ=00or lim fCJ= -0 True O Fo lse

A: