Is there a value of a for which limx1 3x^2+ax+a+3/x^2+x-2 exists? Enter the value of a if such a exist otherwise enter 0.

Q: Prove that lim +1) = 3 using the e--definition.

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Q: 1-z = ? What is lim %3D !- 2!- -2

A: In order to evaluate the limit of a function f(x) at certain point a then replace x by a to get…

Q: 1 Find lim +3 using limit rules. 2.

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Q: (2x-1)(3-x) is (x-1)(x+3) limx→0

A: Given problem is :

Q: Show that lim(5x+2)=-18 x-> -4

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Q: Suppose lim, =1. Prove that lim -(-1)* = %3D

A: Given: limn→∞ an=1To prove: limn→∞ 1n ∑k=1n -1k a2k=0

Q: find the limit of  limx->-4 [(x2-2x-24)/(x+4)]

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Q: How do I compute  limx→4(x^2−6x+8/x^2−4x)

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Q: I am trying to figure out the answer to this problem using L'Hopital's rule. please show all steps.…

A: Given,           limx→02xx+3-3

Q: prove limx->a 1/x = 1/a with epsilon-delta definition

A: We need to prove the given problem using the epsilon-delta definition.

Q: Prove that lim, = 1, (x > 0).

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Q: find the limit or explain why it does not exist.

A: Limit functions generally have indeterminate forms meaning after putting the limit at some point,…

Q: show that : Limx→0    1/ (x – 1) + 1/( x + 1)  ) /x = −2

A: apply the concept of limit to prove the given problem.

Q: What is lim 2 (x - 2)

A: Given

Q: Calculate the limit limx→0lncosx3√1+x2−1.

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Q: find: a) Lim x4-1 x2 b). Lim 10x-3 SinX

A: We have to find the following limit      alimx→1x4-1x2-1       blimx→010x-3sinxx

Q: In(x-2) 1- Find , limx→2 In(x² -4)

A: Answer and explanation is given below...

Q: /1+x – /1 – x lim |æ|

A: Proceed as shown below...

Q: Find limx→−∞(x2 −1)e4x. Show work.

A: We need to find : limx→-∞(x2-1)e4x

Q: Suppose neither limx→0 f(x) nor limx→0 g(x) exists. Show that limx→0 [f(x)g(x)] may exist.

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Q: Show that 4z2 z2 +1 1 (b) lim- z→1(z – 1)3 (a) lim : 43B = 00; (c) lim = 00. - - z(I – 2) 0+2 I- 2…

A: We will use the simple calculations using some usual formulae to evaluate these limits.

Q: Find lim,x - Vx²+ 2

A: To find the limit

Q: lim (In 2x + 5) + 4 X-1

A: From the given problem:   limx→-1ln2x+5+4   As we know that:   limx→afx±gx=limx→afx±limx→agx

Q: lim (In w-

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Q: x² – r3 lim - 2x2 + 3

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Q: : limx->0(1/x3)

A: We have to simplify the given expression. The given expression is limx→01x3∫0xt2t4+1dt

Q: if limxn = x, limyn = y, proof: limxnyn = xy.

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Q: Evaluate the limit limx→∞ √3+11x^2/3+10x

A: Given, limx→∞3+11x23 + 10x Divide the numerator and the dinominator with x, limx→∞3x+11x23x + 10x…

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: х —9 Determine lim V6 - Vx-3 x→9 |

A: HERE WEMUST KNOW ABOUT L'HOPITAL RULE

Q: calculate the limit limx--> ∞ 3x^2+x-1/4x-7

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Q: Vax +9-3 lim What is the value of a if 3D1?

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Q: Show that

A: Here we have to show that;  limx→-∞1x

Q: You are not allowed to use L'Hospital's Rule 2x2 – 32 - lim V3x + 4

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Q: y = b Retrieved from:basiccalc_initial_release_13june.pdf 1. lim b 2. lim エ→1.2 3. lim b エ→ー1

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Q: Use L'Hopital's Rule to evaluate a) lim XXX b) lim X-2 2x e 4x 2x²-5x+2 5x²-7X-6 2

A: Let f(x) and g(x) are two continuously differential function at point 'c'. Then,…

Q: Find the limit or determine that the limit does not exist limx→∞ (2-x)/(√4x2 + 13) 4x2 + 13 is all…

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Q: Show that lim -e-* = 0

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Q: In(x-2) 1- Find , limx→2 In(x²-4)

A: The given limit is, limx→2ln(x-2)ln(x2-4)

Q: of

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Q: If limx→0+ ƒ(x) = A and limx→0- ƒ(x) = B,find limx→0+ ƒ(x2 - x4)

A: Given: limx→0+fx=A, limx→0-fx=B we know that when x=0+, f0+2>f0+4 so, given limit will be…

Q: Prove that limx→3 3x − 7 = 2 by using , δ definition of limit

A: to prove the limit by definition

Q: Show that lim- e +1 does not exist. 1/x

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Q: To determine To find: The value of lim ( - →5 12-41-5 6(1-5)

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Q: Determine limx→−2 6/x-2, if it exists

A: limx→−2 6/x-2 yes limit exist and we can direct apply the limit so put -2 in given function…

Q: lim x in (It -)

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Q: We have lim I- a Vsing 1-x = (- Fa)(+Ta) So, lim 1- Fa lim - a 거- (1-「 (i+Tx) %3D lim ス→) as 1+ T…

A: Yes your solution is correct

Q: What is lim e7-1 Provide your answer below:

A: The objective is to find the limit.

Q: ¤ – z² lim +1 1- ya

A: Here we find limx→1x-x21-x.

Q: Use e-5 definition and prove that lim (2 5r) -6

A: Here we use basic definition of epsilon and delta .