r-1| limr→1 2r-2

Q: Determine the following limits analytically.

A: Given: L=limx→-1x2+8-5-4xx3+1 For evaluating given limit, we substitute x=-1+h, h→0 So,…

Q: XY – 2x - lim (x,y)→(0;2) x² + y² – 4y + 4’'

A: Given:

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: Use the Squeeze Theorem to find the following limit when b |x- al s f(x) s b + |x- al. lim f (x)…

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Q: Evaluate the following limit, or state that it does not exist: sin a/a3 + 9x2 limg40

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Q: Evaluate the following limit: (x- 2)2 – 4 | lim If it does not exist enter DNE.

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Q: 8x? — 4х +1 lim * 2+x-5х?

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Q: Find the limit (if it exists) of A"x, as n approaches infinity, where and x, = a

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Q: Evaluate the following limit 5 - Va lim z+0 5 + Vx Answer:

A: We have to find the limit of limx→∞5-x5+x We know x is strictly increasing function in the interval…

Q: valuate the following using basic limit theorems. V2z + V3 lim 3 422 – 9 -

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Q: 4. Does the following limit exist? ry?-1 lim (zu)(1,1) y -1

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Q: Evaluate the following limit: x3-ze?y lim (x,y,z)-(-1,0,4) 6x+2y-3z .A 5 18 .B .C -5 12 .D 12

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Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 3 lim 4 + 6A

A: We need to evaluate the value of given limit

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: Determine whether the following limits are finite, ∞, or −∞. If the limit does not exist for any…

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

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Q: Evaluate the following limit: 4x2 – 4y? tan(4x4 + 4y4) 8x4 + 8y* - lim (2,y)→(0,0) 1 2 4 The limit…

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

A: The given function can be redefined as follows: 2x+2x,     x<02x-2x,     x≥0

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

A: use the l hospital rule for finding the limit.

Q: Find the limit, if it exists. (I |x + 2| lim x--2 5x + 10

A: Given, The limit limx→-2x+25x+10  We have to find the limit.

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 a limit does not exist, type "DNE". V9 +h – 3 lim h>0 h

A: To find the value of the  given limit first we rationalise  the given function by multiply and…

Q: Evaluate the limit using the Basic Limit Laws

A: Given: Let y=limt→43t-14t+1 To Find: To evaluate the given limit.

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: Find the indicated one-sided limit, if it exists. (If an answer does not exist, enter DNE.) x + 2…

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Q: Use the Squeeze Theorem to find the following limit when c = 0, 2 – x² s f(x) < 2 + x². lim f(x)

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Q: Use the Squeeze Theorem to find the following limit when b - |x-al ≤ f(x) ≤ b+ x - al. lim f (x) I-a

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Q: lim

A: We have two sided limit from the graph

Q: Evaluate the following limit: lim (7,y)→(0,0) 5æ6 + 6 sin°(y) 14x6 + y6 3 4 11 15 2 3 The limit does…

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Q: Use the Squeeze Theorem to find the following limit when b – |x – a| < f(x) <b + |x – al. lim f (x)

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Q: Find the limit (if it exists) of Anx1 as n approaches infinity, where

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Q: Evaluate the limit, if it exists.

A: Given:          limh→0(x+h)3−x3h

Q: Determine the following limit, using oo or - 0o when appropriate, or state that it does not exist.…

A: Given limit is  limx→3+x+4x-3 x→3+ ⇒ x=3+h , With h→0

Q: Use the Squeeze Theorem to find the following limit when b - |x - al s f(x) sb + x - al. lim f (2)

A: 1.b-x-a≤f(x)≤b+x-alimx→af(x) Note:     Multiple questions are given, we are answer with only one…

Q: 1 1 2 lim r→-2 х3 — 8

A:

Q: Use the Squeeze Theorem to find the following limit when b − |x − a| ≤ f(x) ≤ b + |x − a|. lim…

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Q: Evaluate the following limit, if it exists: lim (x,y)>(0,0) x² + xy+ y²

A: We have to evaluate the limit lim(x,y)→(0,0)x3-y3x2+xy+y2 if it exists.

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

A: Given limx→3-2x+8

Q: Vx+3- V3 lim c)

A:

Q: Evaluate the following limit: x3-ze?y lim (x,y,z)- (-1,0,4) 6x+2y-3z .A .B -5 12 .C 5 18

A: Given that  The limit is

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: x*-7x²+x b) lim x→00 x3-x+10

A:

Q: Find the indicated one-sided limit, if it exists. (If an answer does not exist, enter DNE.) lim (6x…

A: limx→1- (6x-4)put x→1- in given equation then we get6(1-) -4

Q: Evaluate the limit, if it exists.

A: Given,  limu→24u+1 - 3u - 2 When we apply the limit directly into the function we will get 0 in…

Q: Evaluate the following limit numerically, or show that it doesn't exist

A: Here, we substitute h=x-2, as x approaces 2, then h approaches 0 , we substitute the x=h+2 in given…

Q: Show that the following limit does not exist: (x – y²)2 lim (r,y) (0,0) ² + y4

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Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x2 + 4x + 3 lim x - -3…

A: