Suppose that lim a, = 1, lim b. = -1, and 0 < -b, < a, for all n. Evaluate the limit. (If an answer does not exist, enter DNE. If there is not enough information to determine whether the limit exi enter NOT ENOUGH INFORMATION.) lim 3a, - 4b,

Q: b) Now, follow an algebraic approach to compute the limit 13 – 1 lim 1 I-1 and the limit V9+x– 3 lim

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Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) -1 lim (-6 +h)-¹ + 6-1…

A: L'Hospital rule:- If limx→0f(x)g(x) is of the form 00 then limx→0f(x)g(x)=limx→0f'(x)g'(x)Continue…

Q: (a) By using the definition of limit, prove that lim (3x+i z31

A: Introduction: Limits in mathematics are distinct real numbers. Consider a real-valued function "f"…

Q: Use the precise definition of a limit to prove the following limits. Specify a relationship between…

A: In the given question. We have to first check whether the function has indeterminate form if the…

Q: Find the limit, if it exists.

A: limx→-∞x4-1x3-1=-limx→-∞x4-11-x3 We have limx→-∞x4-1=∞limx→-∞ 1-x3=∞ So by  L'Hospital's Rule, we…

Q: Prove, using the e-d definition of limit, that: (a) lim x² + 1 = 2 24-1

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 8. 8 lim

A: First, we factor the denominator limt→08t-8t2+t=limt→08t-8t(t+1)=limt→08(t+1)-8t(t+1)  [used…

Q: Consider the following. lim (4 – x) X→3 y 3 2 1 2 4 Use the graph to find the limit (if it exists).…

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Q: Evaluate the limit, if it exists. ( 6. lim t-0\ 을) tV1+t

A: We have to evaluate the limit: limt→09t1+t-9t Since it is ∞-∞ so simplifying  the limit, Taking 9…

Q: Find the limit. lim (tth)" 4.

A: Take the common terms out from the numerator.

Q: Determine the value of the following limit, if it exists. If infinite, specify either o or -o. (If…

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Q: r-1| limr→1 2r-2

A: We have to find

Q: Define x,, X1, x2, . .. as follows: 2 + Xg - 1 for each integer k > Xo = 0 Find lim x,. (Assume that…

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Q: lim,(1+ 1 = e

A: To prove the given limit

Q: - What is the limit of lim 5*? X--00 A. -00 В. О С. 1 D. +00

A: limx→2 x3+13=23+13=93=33=1

Q: Is there a real number a such that 3r + ar + a+3 lim --2 r+x + 2 exists? If so, find the value of a…

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Q: Prove, using the e-8 definition of limit, that: (a) (b) lim ²+1=2 24-1

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Q: Evaluate the limit, if it exists. If a limit does not exist, type "DNE". V4 + h - 2 lim h>0

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Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) V81 + h - 9 lim

A: 6. The given limit is, limh→081+h-9h. Note that, the given limit is in the indeterminate form. Apply…

Q: When proving the limit lim(x² + 4x - 1) = 11, and e > 0 is given, what is an appropriate choice for…

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Q: Find the following one sided limit -5 lim z→1+ £ – 1

A: here we have to find limit from right hand side

Q: 1 lim ty1 + t

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Q: Find the limit. (If the limit is infinite, enter 'co' or '-co', as appropriate. If the limit does…

A: Our Aim is to find the limit of the expression given below:-limx→∞x+2x26x-1-(i)

Q: Find the limit. (If the limit is infinite, enter 'o' or '-∞', as appropriate. If the limit does not…

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Q: Find the limit, if it exists. (1+h}l/3_ 1 lim h-0 Does not exist 1/3 3.

A: We will find the limit as following.

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 2 2 lim

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

Q: Evaluate the limit, if it exists. (If an answer does not exist, erter DNE.) V 25 + h - 5 lim h - 0

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Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) (2…

A: We have to calculate value of given limit.

Q: Find the indicated one-sided limit, if it exists. (If an answer does not exist, enter DNE.) lim (9Vx…

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Q: Evaluate the limit, if it exists.

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Q: Find the limit, if it exists. Vx² – 5 lim - 5 7x – 1

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Q: Use the definition of the limit (e – 8) to show that 1 lim - = i. 2+-i z

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Q: Find the limit, if it exists. If it doe 3a + 3x + 4 lim 202 + Enter your an Enter DNE fo

A: We have to find  the limit .

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 9 lim 1 +t

A: We have to find limit

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) V 16 + h - 4 lim

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Q: Find the limit, if it exists.

A: It is given that, limx→∞xx2+1We have to find the limit,if it exists.

Q: Consider the following. lim (4 - x) X-3 y 3 1 2 4 Use the graph to find the limit (if it exists).…

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Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) 2x2…

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Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) 2x2…

A: We have expression as limx→22x2+13x-2   It can be written as limx→22x2+13x-2

Q: Use the precise definition of a limit to prove the following limits. Specify a relationship between…

A: To Prove - limx→3 x2-7x+12x-3 = -1Cosidering LHS - limx→3 x2-7x+12x-3 = limx→3 x2-3xx-4x+12x-3limx→3…

Q: Evaluate the following limit, if possible. If the limit does not exist, type DNE. 4-x 4 lim 42-√√

A: Given limit limx→44-x2-x. The objective is to evaluate the limit.

Q: Use the precise definition of a limit to prove the following limits. Specify a relationship between…

A: Given limx→3-2x+8

Q: Find the limit. (If the limit is infinite, enter '' or '-', as appropriate. If the limit does not…

A: We need to find the limit of                                  . So,                   limx→∞…

Q: x2 + x – 6 lim х — 2

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Q: Use the definition of the limit (e – 8) to show that 1 lim = i. z-i z

A: Limit Definition: Let f(z) be a function defined in some neighbourhood of z0. A complex number w0is…

Q: Find the limit lim,→+∞In(x² – 4) – In(x + 2)] Enter I for o, -I for –∞, and DNE if the limit does…

A: Given, limx-&gt;inf [ln(x²-4)-ln(x+2)]

Q: Evaluate the limit, if it exists.

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Q: find the limit, if they exist.lim x-&gt;a (x^2+x-6)/x+2

A: Here, two cases arises, if a=-2 ,then denominator of function is zero and limit does not existIf a…