If lim an and lim b, do not exist, then lim (an + bn) does not exist. n00 n 00 n00

Q: If lim a, = 0, then lim an = 0. 72-00 72-00

A: We have to check

Q: Use divect substitution to venty that the Lòmit below Leads to an intermediate firm. Then use…

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Q: 3x3 +4x2 -x-2 x>-1 2x3 +5x2+4x+1 Use L'Hospital's Rule to evaluate lim

A: Given data:   The expression for the limit is limx→-13x3+4x2-x-22x3+5x2+4x+1.   Substitute the given…

Q: Vx- 2 Evaluate lim x-8 x2-7x-8 O 2/7 None of these O 1/9 O 1/12 O O o O

A: The given limit,     limx→8x3-2x2-7x-8

Q: 1. If lim an = a then lim an+10 lim an–10 = a. n-00

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Q: 5. Prove that lim x+0+ x3 (HINT: This proof needs a B–8 type argument.) = 0 and lim x→0- x³ ||

A: please see the next step for solution

Q: Evaluate lim a br lim (1 + 4)*

A: We use L hospital rule

Q: If lim an = L, then lim an+1 = L + 1. n→∞ n→∞

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

Q: If lim f(x) = -5, lim f(æ) = 2, lim g(x) = -1, and lim g(x) = 4, then the limit lim (2f(x) – 39(x) +…

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Q: an+1 . Recall the special case of the ratio test, which is inconclusive if lim equals one. Prove an…

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Q: (ii) Using Sandwich theorem, find lim g(x) xsinx 1 6 < 1 2 – 2cosx -- - holds for all values of x…

A: The sandwich theorem states that if fx≤gx≤hx for all x∈R and fk=hk for x=k then fk=hk=gk.

Q: If lim an 72-00 lim a2n+1 n-00 L, then lim an = L 11-00

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Q: 1+2+...+n 2. Let n be a positive integer. Evaluate lim if possible. If not possible, explain n2 n 00…

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Q: n is not a negative integer Given n ≥ 0; justify that limx->∞ fn (x) / ex = 0

A: The limit of the given function goes to zero as the exponential function goes faster to infinity…

Q: (-x+ 2, x 0 not, why?

A: The given function is: g(x)=-15x+2,  x&lt;0-2,            x=0x+2,         x&gt;0 From the definition…

Q: (1+x)* - b. Evaluate lim

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Q: If lim a2n = lim a2n+1 = L, then lim an = L 72-00 11-00 11-00 where L is equal to Blank 1. Blank 1…

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Q: √x-3 x-3+√√√x²-9 Evaluate lim

A: Given query is to find indicated limit.

Q: proof that it An then Lim ヘーつ it And then Lim かy

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Q: Which one is correct, and which one is wrong? Give reasons for your answers. a. lim lim b. lim 6.…

A: If we plug x=3 in the given expression then we get:

Q: lim sup (an + bn) lim inf a, + lim inf b, n→∞ n→∞ n→∞

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Q: Fina the llmit or State that the lmit does not exist li Lim (I+ * 2. Lim (I+2X)

A: Explanation of the answer is as follows

Q: If lim an = 12400 lim a2n+1 = L, then lim an = L 11-00 11-00

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Q: x2-6x+5 1) lim (* Show all work below to evaluate the limit. x3 -25x x-5

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Q: (会 lim 4x - 1 Find a. 2x + 5 lim 3x + 5 - 6x - 8 2x lim b. Evaluate + x - 12

A: a) limx→-∞4x-12x+52b) limx→-22x-6x2+x-12+limx→∞3x+56x-8

Q: If lim an = 0, then the answer to lim a, is Answer:

A: Please solve two small question

Q: We are trying to prove a certain limit. One of the steps in the proof is to show that for every &> 0…

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Q: An+1 7. Recall the special case of the ratio test, which is inconclusive if lim equals one. Prove An…

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Q: 1. (a) Suppose that lim an = L. Tell in a complete sentence why lim an+1 = L. n00 an+1 (b) Suppose…

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Q: if x + -3 f(x) х+ 3 a = -3 1 if x = -3 lim f(x) and lim f(x) are finite, but are not equal. | x→-3+…

A: Left-hand and Right-hand limit is given as: LHL=limx=a-hfxRHL=limx=a+hfx The limit exists at x=a, if…

Q: OHence or otherwise find esinx – 1+ In(1 – x) lim x-0 x²sinx

A: (b)-

Q: 2x-128 Evaluate lim or show that it does not exist. x - 2 x4

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Q: An+1 If am = (-3)" for all n > 0, then the value of lim is An n-00

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Q: Find all values of p so that lim x->2 (px^2+ 15x+ 15 +p/x^2+x-2 )exists

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Q: n2 Find lim if it exists. Be sure to show all of your work. n-00 en 2.

A: topic -limits

Q: 3. Given: lim f(x) = 6 and lim g(x) = 3 a. lim [4g(x)] =

A: It is given that limx→cfx=6   and limx→cgx=3

Q: lim inf[0, n/(n +1)) = lim sup[0, n/(n + 1)) = [0, 1). %3D We can now give an interpretation of lim…

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Q: 3x* - 4x2 +3x – 6 Evaluate lim x-0 5x- x2 – 3x5-2x -1 does not exist O 1 O None of these

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Q: lim f(x) = c0 and lim f(x) = -0, which of the following statement(s) is/are true about lim f(x)? lim…

A: The limit limx→1fx exists when the left hand limit limx→1-f(x) and right hand limit limx→1+f(x) must…

Q: 1+ 2+...+n 2. Let n be a positive integer. Evaluate lim if possible. If not possible, explain n2…

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Q: 5- 3x? Evaluate lim x-00 (2-x) (x+ 2) does not exist O NONE OF THESE -3 3 O O o O O

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Q: where L is equal to Blank 1. Blank 1 Add your answer If lim azn = lim a2n+1 = L, then lim an = L…

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

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Q: f(x)-4 If lim 2, then lim f(x) = %3D x-1 x→3

A: Given,  limx→3f(x)-4x-1=2

Q: lim 1+ Find (if it exists)

A: Given: limx→∞1+1xx

Q: x+5-2 lim lim_1. Then f(-4) is ? X--1f) can be rewritten as x+1 X+ -1

A: Given that: limx→-1x+5-2x+1 is written as limx→-11f(x).

Q: 4- x2 Evaluate lim x+2 3- (x2+5)Z 5 3 O NONE OF THESE O 4

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Q: (n - 1)1 lim an

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