X -1 lim х - 1 X-1 X,

Q: Determine the infinite limit. x + 2 lim x--3+ x + 3

A: We have to determine infinite limit: limx→-3+x+2x+3 We know that finiteinfinite=0finite0=infinite

Q: Vx+2-1 lim х>-1 х+1

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Q: Find the limit (if it exists). If the limit does not exist, explain why.

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Q: limに 1 x2-3x+2 X-1 x-1

A: We have to find

Q: e2x -1 Use L’Hopital's Rule to find the limit. lim

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Q: Thoroughly explain how to determine when a limit does not exist.

A: The limit does not exist when after applying the limit to a function the function attains infinite…

Q: find the limit or explain why it does not exist. 1 - Vx lim 1- x

A: we have to find the limit . limx→11-x1-x

Q: Evaluate the limit. hr lim (1+-

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Q: lim Vx +x+1 x- - X-∞

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Q: . lim (3 – 2e

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Q: How does the sandwich theorem enable us to calculate a variety of limits?

A: Sandwich theorem: Consider 3 function f(x),gx,hx such that fx≤gx≤hx. Also, assume that limx→cf(x)=L…

Q: How would this process look should we try to do it via limit definition (IE, (f(x+h)-(fx))/h)?

A: Derivative of g(x) at x=a=limh→0g(a+h)-g(a)h

Q: find the limit or explain why it does not exist. x'/3 – 1 lim iVx – i Vx – 1

A: The given expression is limx→ 1x13-1x-1

Q: Find the limit is it exisit.

A:

Q: Find the limit, if it exists. If the limit does not exist,explain why.

A: x→-2lim2-|x|2+x=x→-2lim2+x2+x=x→-2lim1=1

Q: Differentiate the power function f(x)=x4 using the limit definition.

A: Given: fx=x4

Q: Find the limit (if it exists). If the limit does not exist, explain why.

A: Given: limx,y→1,1xy-11+xy for finding given limit, we substitute x=1, y=1 in given expression

Q: 2sin()-1 limx¬1- X-1

A: The given limit is limx→1-2sinπx3-1x-1

Q: Evaluate the limit using the Basic Limit Laws

A: To find the limit  limx→5x-2

Q: x -1- V3x +1 V3x + 1 lim x-5 x - 5

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Q: 1 (i) lim

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Q: cot3x Lim X-o cotx 0

A: Given limx→0cot3xcotxTo evaluate the limit:

Q: Evaluate the limit using the Basic Limit Laws

A: We have to evaluate the following limit: limx→-13x4-2x3+4x

Q: Evaluate the limit or determine that it does not exist.

A: To evaluate the limit lim(x, y) → (3, 4) 1x2 + y2.

Q: V2x –1 Using defination of limits, prove that lim Vx- 3 L^ = X4

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Q: lim |x-

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Q: Calculate the limit for the function f(x) = 33 – 11x and interval [2, 6]. Verify your answer by…

A: Given that: f(x)=33-11x in [2, 6]

Q: Determine whether the limit lim Vx² +1– Vx+1 exists. Please explain your answer.

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Q: lim - Va +1

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Q: Find the limit if it exist.

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Q: Jx +3 Find the limit. If it doesn't exist, explain why. lim x->9 x-9

A: limx->9x+3x-9

Q: Evaluate the limit, if it exists.

A: The given expression is limx→-2x+2x3+8

Q: Find the limit (if it exists). If it does not exist, explain why.

A: To evaluate the limit: lim△x→0-1x+△x-1x△x. Here, x will be treated as constant. When we put the…

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

A: Given: limx→11-x1-x for evaluating given limit, we factorize denominator and find limit

Q: Explain why the limit does not exist. X lim X-OX

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Q: Find the limit, if it exists. If the limit does not exist, explain why. lim,2 1-2?

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Q: Find the limit. Enter the exact answer. If the limit does not exist, indicate that using the check…

A: limx→∞sin-14x6-8x=sin-1limx→∞4x6-8x=sin-1limx→∞4xx6-8xx , [divide both numerator and denominator by…

Q: lim 4x3 5x3– - ×ーフ。 2x² -1

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Q: Find the limit or show that it doesn't exist. 1-х-х2 a) limx→-o 2х2-7 V1+4x6 b) limx 2-х3

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Q: Find the limit. Enter the exact answer. If the limit does not exist, indicate that using the check…

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Q: Evaluate the limit, if it exists. If not, determine whether the one-sided limits exist (finite or…

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Q: Evaluate the limit, if it exists. lim (1/4+1/x)/(4+x) x--> -4

A: The given expression is,

Q: Use L-Hospital Rule to find the limit as x goes to infinity (1-(3/x))^(2x).

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Q: evaluate the limit, do not use lhopital's rule 1-x+2x+7 limx→-x 2 V 9x +5 - 3x

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Q: Find the limit lim 4-V X-16 16x-x2" if it exists. Use Limit Laws if possible.

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Q: Determine the infinite limit: lim (x – 3)5 I-3-

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Q: (a) Find the limit (if exist): lim "(2t-2)2 dt 2x-1

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Q: Explain why a limit of the form 0∞ is not an indeterminate form.

A: The only indeterminate forms are: 0/0 ∞/∞ 0 · ∞ 00 ∞0 1∞ ∞ - ∞

Q: Find the limit if it exists.   lim(x,y) ---> (0,0)     (x4-16y4)/(x2+4y2)

A: Given: limx,y→0,0x4-16y4x2+4y2

Q: Find the limit (if it exists). If it does not exist, explain why.

A: Given: lim△x→0+x+△x2+x+△x-x2+x△x