an 2. Suppose that lim : 2. Show that lim an = +. n00 n n00

Q: The value of lim in is nº (1+ n00 (1) e (2) e? (3) Ve (4) e 1

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Q: +∞o Suppose Στ% από = 5. What is the value of lim an? n-0

A: Here we use the theorem of convergent series to determine the limit.

Q: Given that lim a, = a, find the limit a and determine N so that a, -al < n-00 1 an e= 0.02 1 lim…

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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: Suppose that lim f (x) = 3 and lim g(x) = 5. Then lim + 2f(x)g(x) x2 x-2 10 O 20 O 30 No answer…

A: We have given that limx→2f(x)=3 and limx→2g(x)=5. We know that if limx→af(x) and limx→ag(x) exist…

Q: Which of the following is/are signified by limx→af(x)=∞limx→af(x)=∞? The limit exists and equals…

A: Which of the following is/are signified limx→af(x)=∞?

Q: If 0 < a <1, then lim(a)* = x00

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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: b ax + x2 Evaluate lim where a>0

A: Limit of given function is solved.

Q: Suppose f(r) is a function, and that lim f(r) = A +7- and lim f(z) = B. (a) If I tell you that lim,…

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Q: If lim f(x) =L, then lim an = L. n-00

A: Given: Let an be a sequence and f be the function such that f(n)=an for n≥1 Also,  limx→∞f(x)=L To…

Q: following limit Find the lim sh(7e) 5x

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Q: tan r 1 The value of lim is Select one: O a. а. е O b. 1 O C. -1 O d. 0 /-

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Q: Find lim an if an = n!+3" 1+n OA. 0 B. C. 00 D. OE. 1

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Q: If lim f(z) = o and limg(z) = 00 , then lim (f(x) – g(x)) 0. Select one: O a. False O b. True

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Q: After direct substitution the limit lim (cschx) gives X+00 Select one: 0° O None

A: We have to find after direct substitution of limit

Q: How do you solve num 5?

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Q: Find a function f and a number a such that (2+ h)6 – 64 lim - f'(a). h→0 h

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Q: find the lim as n goes to infinity, where a1=2, and the given equation is a(sub)n+1=(1/2)*(a(sub…

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Q: +6 If q(x) = find lim q(x). Provide your answer below:

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Q: Find the limit, if none, kindly write DNE. lim of x over x^2-16 as x approaches to 4^plus(+

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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: After direct substitution the limit lim (cosx)cscx gives x-0+ Select one: O None O 01 O 10 O 00 O 0*

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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: 1 2) Let f (x) = 3+ 4x-8 Find the following: %3D

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Q: Evaluate the following limits. a. lim?→3 √x^2 −5−2  b. lim?→64 3√x−4  / √x−8

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Q: (a) lim f(x)= (b) lim,-2+ f(x) = (c) lim f(x) =, (d) Is f'(3) is positive, negative, or zero? (e) Is…

A: We will solve the problem

Q: Find lim (1 +

A: We have to find

Q: z2 - 3 if r 2 3 (a) Calculate lim f(z) and lim f(z). Make it clear which limit is which. +2-

A: x→2+ means x is little more than 2.So, limx→2+f(x)=limx→2+(3x-5)=3(2)-5=1

Q: Suppose that lim tg(t) = 12. Show that lim g(t) exists and equals 4. 1+3

A: Assume g(t) = 12t, so that limt→3tg(t)=12

Q: Suppose you know • lim f(æ) = o and lim g(x) = o. • lim f'(2) = - 4 and lim g'(x) = 7 %3D * 00 2…

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Q: For the limit illustrate Definition 6 by finding values of N that correspond to

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Q: If 7- 4x s g(x) s7 cos x for all x, find lim g(x). lim g(x) = X-0 (Type an integer or a simplified…

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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: If lim g(x) = 13 and lim h(x) = 23 then %3D [39(x) + 6h(x)] lim x6 2 O 26 O 88.5 O 46 O 36 O 19

A: The limit of a function at a point exists if both left-handed and right-handed limit exist and are…

Q: 12. Let L = lim a>0. If L is finite, the (A) a=1 (B) a=2 (C)L- (D) L-

A: We are asked to find a value and L values.

Q: 5.8. Show that if lim f(z) = wo, then lim f(2)| = |wo|.

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Q: Find the following limits : 3) lim x 2 + 32 - (주

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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: 5 In evaluating 35₂ dx , is same as evaluating lim (In(f(x))). Determine the value of f(x) if…

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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: If lim f(x) = 14 and lim g(x) = 25 then lim [2f(x)g(x) – 6] = %3D O 28 O 706 O 700 O 694 O 178

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Q: Which one is correct, and which one is wrong? Give reasons for the answers. X-3 1 = lim - =- X-3 (a)…

A: Given: limx→3x-3x2-3

Q: 37 5 If f(x) = 2x + 5x then 3 lim f(r) =

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

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Q: In evaluating S dx is same as evaluating lim C-3+ (In(f(x))). Determine the value of f(x) if x=3.4.

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Q: Which of the following is/are signified by lim f(x) = 0? O The value of f(x) becomes infinite when x…

A: limx→af(x)=∞To find its meaning

Q: Evaluate I (n +) lim as n → ∞ VnT (n + 1)

A: Given: limn→∞Γn+32nΓn+1