Explain what it means to say that lim_ f(x) = 4 and lim f(x) = 1. x- 2* O As x approaches 2, f(x) approaches 1, but f(2) = 4. O As x approaches 2 from the left, f(x) approaches 4. As x approaches 2 from the right, f(x) approaches 1. O As x approaches 2, f(x) approaches 4, but f(2) = 1. O As x approaches 2 from the right, f(x) approaches 4. As x approaches 2 from the left, f(x) approaches 1. In this situation is it possible that lim_ f(x) exists? Explain. X-2 f(x) could have a hole at (2, 4) and be defined such that f(2) = 1. Yes, O Yes, f(x) could have a hole at (2, 1) and be defined such that f(2) = 4. O Yes, if f(x) has a vertical asymptote at x = 2, it can be defined such that lim_f(x) = 4, lim_f(x) = 1, and lim f(x) exists. x-2 x-2* X-2 No, lim f(x) cannot exist if lim_f(x) # lim_f(x). X-2

Q: Find the limit of limx->-1 (x3-2x2+5)

A: Since this is a polynomial function,we can calculate the limit by direct substitution. We have The…

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

A:

Q: Find the limits in Exercise

A: We have to find the limit of the function: limx→3-x2+8x-7 This is determinate limit so we need to…

Q: Next, we check the limit when approaching from the right. As x approaches −10 from the right, we…

A: The given limit is ,limx→-10+5x+50x+10

Q: Find the limit or determine that the limit does not exist limx→0 (1/(x√1+x) - 1/x) 1+ x is all…

A: The given function is, Simplify and rationalize the numerator of  the given function as follows.

Q: 6* - 2* lim,

A:

Q: What can we conclude about lim(x,y)->(0,0) f(x,y) from the given function and its level curve graph?

A: General equation of curve along any c is yx=c. Thus get equation for y2: yx=c  y2x2=c y2=cx2

Q: Evaluate the limit and express your answer in simplest form. \lim_{h\rightarrow 0}\frac{\arctan…

A:

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: SOLVE BY LIMIT DEFINITION 3x+1 2-x a) limx-2+1 limx→

A: Solution

Q: Calculate the limit limx→13√x−1x−1.

A:

Q: Evaluate the limit. +4-2 limx→0

A: First rationalize the numerator.

Q: Find the one-sided limit (if it exists).

A: Given We have to evaluate given one sided integral.

Q: If lim f(x)=-2 x-->0+, lim f(x)=3 x-->0-, and f(0)=-2, what can you say about lim f(x) x-->0?

A:

Q: Determine the Limit:  Limx->infinity (1/8)x

A: Consider the given problem:

Q: 2. Explain why f(x, y) must approach a unique number L as (x, y) approaches (a, b) along all paths…

A: A number L is said to be the limit of a function f(x,y) as (x,y)→a,b , if for any real number ∈>0…

Q: Use definiction to १r० v of Conkegene to lim n+4

A:

Q: Determine the infinite limit. (а) lim (x – 3)5 x→3-

A:

Q: Estimate the value of the Limits 2x 2x lim -3+ x 3 and lim x-3 X-3 |

A:

Q: How do you evaluate the limit:  limx-->0  (sin(4x))/9x WITHOUT using L'Hospital's Rule?

A: A property:L'Hospital's Rule is not necessary here.The following is an important property used in…

Q: Determine the infinite limit limx→2− x^2 − 2x/ x^2 − 4x + 4

A:

Q: 2 lim x→1- x²

A: The limit of the function f(x) is obtained as L=limx→a-f(x)L'=limx→a+f(x) Then the limit of the…

Q: use definition of limit to show:   lim    (4x + 1) =13 x->3

A: The definition of limit:

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

A:

Q: Find the limit using direct substitution. lim                      3x+1/2-x x-->-2

A: In the direct substitution method, straight way substitute the limiting vailue of x in the given…

Q: what is lim of x approaches -8 from the left of 7x+56/abolute value of x+8

A:

Q: Find the one sided limit, lim-0

A: We solve the limit.

Q: Find the limit as x -> (+) or (-) oo (Infinity) using L'Hoptials Rule for: Lim as x->oo of (9x +4)…

A:

Q: compute the limit (or state that it does not exist) assuming that lim n→∞ an = 2

A: Answer :  Limit does not exist. Explanation : Here I am attaching the screenshots of the solution

Q: х +7 lim х-3 (x — 3)2

A: For the limit to exist, it must be unique and finite.

Q: Prove using the formal definition of a limit that: limx→3 (2x + 2) = 8

A: Given limx→3(2x+2)   = 8Right hand limitlimx→3(2x+2)Let x = 3+h    where h→0hence limh→0(2(3+h)+2) =…

Q: Evaluate the limit 1 lim x--3 (x + 3)²

A:

Q: X -1 lim х - 1 X-1 X,

A: We have to compute the limit  limx→1 x-1x-1.

Q: Estimate the limit numerically  limx→4 √x−4/x−16=

A:

Q: Find the indicated limit able to evaluate. X -5 lim x-5

A:

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

A:

Q: lim x→5 (7x − 6

A:

Q: 2. Use L'Hopitals's rule to find lim (-).

A: Given that: limx→0+1x-1ex-1

Q: estimate the limit numerically to two decimal places or state that the limit does not exist

A: Given limit is  We will evaluate this limit by direct substitution because exists at x=-2, that is…

Q: Suppose that limx→2[f(x)+x2]=α. Find  limx→1(x+1)f(2x)

A:

Q: If lim f(x) = - infinity x-->-1+ and lim f(x)=-infinity x-->-1-, what can you say about lim f(x)…

A: answer

Q: Find the limit. lim sech(x)

A: Given:limx→∞ sechx

Q: Find the limit. x + 3x - 10 lim x+5 x--5

A: It is given that,       limx→-5x2+3x-10x+5 We have to find the limit.

Q: Estimate the limit numerically  limx→4 x^2−2x−8/x^2−3x−4=

A: We have to find limit

Q: Evaluate, use L'Hopital's rule when appropriate:   lim  (eax+x)1/x x->0…

A: Given that: limx→0(eax+x)1/x

Q: Prove the limit. Using the precise definition of a limit. lim x approaches 2 x3 =8.

A:

Q: a) calculate the limit x--> -7 x^2+6x-7/x+7 without using L Hoputals rule    b) calculate lim x-->…

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A:

Q: ) Use the definition of limit to verify lim -3x +2 = –10 x→4

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.