Ag(x)In the graph shown below, why does lim g(x) exist even though g(1) is not defined?x-13\4 5 6The limit exists because as x approaches 1 fromg(x)V 6. Therefore lim g(x) exists even though g(1) is notx-1defined.cesary

For limit to exists at x= a, function must be approaching at a common value from both sides of a.

Ag(x) In the graph shown below, why does lim g(x) exist even though g(1) is not defined? x-1 -2-ib/ The limit exists because as x approaches 1 from g(x) V 6. Therefore lim g(x) exists even though g(1) is not x-1 defined.

Ag(x) In the graph shown below, why does lim g(x) exist even though g(1) is not defined? x-1 -2-ib/ The limit exists because as x approaches 1 from g(x) V 6. Therefore lim g(x) exists even though g(1) is not x-1 defined.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 8E

See similar textbooks

Related questions

Q: 1- Find the limits: lim V - 1 メ→ x-1 а. 2x3 b. lim x- 00 3(x-2)2 2x3 c. lim x2 3(x-2)2 x+1 d. lim…

A: Consider the limits a.limx→1x−1x−1b.limx→∞2x33x−22c.limx→22x33x−22d.limx→3x+13−x2

Q: Find the limit lim x-2

A: Explanation and solutions is given below....

Q: the limits if it exists, if it does not explain why. (1) lim ()" (ii) lim

Q: Given that lim f(x) = 2 and that lim f(x)= -2, does lim f(x) exist, and if so, what is its x→-2…

Q: Because of their connection with secant lines, tangents, and instantaneous rates, limits of the…

Q: V1 +x - 1 Find the limit lim x-0 if it exists.

Q: The process by which we determine limits of rational functions appliesequally well to ratios…

A: Solution:Givenlimx→∞ x-34x2+25To find the limit valueFormula:ab=ab

Q: Consider the limit lim ((x-5)^2*y^2)/((x-5)^4+y^2) being (x,y)->(5,0) does the limit not exist or…

A: Solve the following

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

Q: The process by which we determine limits of rational functions appliesequally well to ratios…

Q: True or False: We can calculate a limit of the form lim f(x) x-->c simply by finding f(c).

A: In general, this is false statement. Answer : False Reason is below:

Q: V-1- x + 2 if x -- 2 Calculate the following limits. Enter "DNE" if the limit does not exist. lim…

Q: B. Find the limit. Зх— 1 5. lim х-1/3 9х2-1 x3- 1 6. lim х+1 х-1 Vx+5 -2 7. lim X→-1 х+1 Vx-1 4. lim…

Q: 5.) Find the limit. When necessary, state that the limit does not exist. x² + 3x-18 lim Xx-3 x-9

Q: 7. Find the limit, if it exists. If the limit does not exist, explain why. sin (2x - 6) sin(4x12)…

A: To find if the limit exists or not. limx→3sin2x-6sin4x-12x2-6x+9 limx→5fx when limx→5fxx-5=3

Q: x2 + x -6 2. Use the precise definition of a limit to prove lim2 x - 2

Q: Determine the limit at infinity. 4 22) lim 9 - (5/x²) X→-0

A: step 2 complete solution

Q: 7. Find the limit, if it exists. If the limit does not exist, explain why. - (a) lim sin (2x 6)…

A: solution is given below

Q: 8 - x- x2 if x 4 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(æ)…

Q: following Rationalisation method: Evaluate the Limit using Vx + 4 – lim- x-5 X - 5

Q: x²-4x+3 Find the limit. lim x²-1

Q: x +1 Evaluate the given limit of lim if it exists. x→-1 x4 – 1 limit does not exist -1

Q: 4-VE Find the limit: lim→16 x-16

A: We need to evaluate the following limit limx→164-xx-16

Q: 5) Does the limit |x+1| lim x-1 x+1 exist? If yes, find its value, if not - explain why. Show all…

Q: Please evaluate the limit.

A: Given,

Q: #20 Find the limit. lim 1-x2 メ→0 x²-x+2

Q: x³ - 3x² + 2x Evaluate lim - using l’Hôpital's Rule and then х — 2 check your work by evaluating the…

A: Given, limx→2 x3-3x2+2xx-2

Q: 1. Evaluate the limit: 5 - x lim x→5+ (x – 5)2

A: Since you have asked multiple questions, we will solve the first question for you. If youwant any…

Q: 4. Find the limit: lim (b) lim -5x+4 x-4 X-4

A: We can find the limit using the L'Hospital rule.

Q: Using: lim f(x) = 4 and lim g(æ) = 8, evaluate f(x) + g(x) 6f(x) lim Answer: Enter DNE if the limit…

Q: 7. Find the limit, if it exists. If the limit does not exist, explain why. Show all work! 2x 1 lim…

A: Given: limx→0.5-2x-12x3-x2 We have to find the value of the given limit

Q: Use lim f(x) = -2 and lim g(x) = 5 to find the limit. %3D lim [3f(x) – 4g(x)]

A: The given limits are limx→cf(x)=-2 and limx→cg(x)=5

Q: 3. Evaluate the limit if it exists: а. lim 8-0 sin-B b. lim(1+x*)*

Q: Find the constant c so that the limit limx->3 (x2+x+c)/(x2-5x+6) exists.

Q: 2. Find the limit of the function (if exists). If the limit does not exist, explain why. For…

A: (b). limx→0 x2+a2-ax2 ; a>0

Q: 18 -a+1 Find the limit lim a9 2x2+3x-1

A: Given, limx→918x2-x+12x2+3x-1 To evaluate limit

Q: 1. If limit of f(x) -8/x-1=10 as x approaches 1, find limit of f(x) approaches 1

A: As per the company guidelines we are supposed to answer nly first question.Kindly repost the other…

Q: How do you solve question 5 and 6?

Q: x² +1 Evaluate the limit of limx ( - ax – b) = 0 - x+1

Q: Find limit lim x--> infinity of f(x)= (1+7/x)x

Q: 3- If lim f(x) = 3.5 and lim,2+ f(x) = 6.5 , the function has a double sided x-2- limit or one sided…

Q: c) lim -4e-x

A: c) limx→∞-4e-xlimx→∞-4ex

Q: 13. (a) Estimate the value of lim- X x+√1+3x-1 X √1+3x-1 By graphing the function f(x) = - (b) Make…

A: Given: 13. f(x)=x1+3x-1 To find: (a) Value of limx→0x1+3x-1 by graphing f(x)=x1+3x-1 (b) A table of…

Q: EXAMPLE 5 A Limit That Does Not Exist numerically. Investigate lim sin graphically and

Q: Find the limit, if it exists. lim x→−∞ (3/x - x/8)

Q: x3-1 Use L'Hôpital's Rule to find the limit: lim x-1 4x3-x-3

A: L'Hopital's Rule- If given to evaluate limx→afxgx and if limx→afx=0 and limx→agx=0 or limx→afx=±∞…

Q: V-1-x +5, if x -2 Calculate the following limits. Enter "n" for a limit which does not exist. lim…

Q: Consider the limits. lim f(x) = 4 x-7 %3D lim g(x) = -18 Evaluate the limit using the limit law for…

Q: Find the limit. lim X→1 lim X→1 √√x² +15-4 2 X-1 2 x + 15 -4 X-1 || = (Type an integer or a…

Concept explainers

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.

Question

Ag(x)
In the graph shown below, why does lim g(x) exist even though g(1) is not defined?
x-1
3\4 5 6
The limit exists because as x approaches 1 from
g(x)
V 6. Therefore lim g(x) exists even though g(1) is not
x-1
defined.
ces
ary

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Limits and Continuity$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

9. Find the value of a such that exists and find the limit. limx-> -1 (2x2-ax-14)/(x2 -2x-3)
Find limit, if it exists. If the limiting value is infinite indicated if its positive or negative a) lim where f(x)= 2x+9 if x is less than equal to 4 x->4+ x^3-6 if x is greater than 4
1. If limit of f(x) -8/x-1=10 as x approaches 1, find limit of f(x) approaches 1 2. If limit of f(x)/x^2 = 5 , find the following limts, a) limit of f(x) as x approaches 0 and b) limit of f(x)/x as x approaches 0. 3. Show by means of an example that limit of ( f(x) +g(x) ) as x approaches zero may exist even though neither limit of f(x) approaches a nor limit of g(x) exists as x approaches a
Find the limit of lim((9+3x)1/2-3)/x as x approaches 0
Find the limit. lim x → 2− e3/(2 − x)
If x4 <=ƒ(x)<= x2 for x in [-1, 1] and x2<=ƒ(x) <= x4 for x <-1 and x> 1, at what points c do you automatically know limx-->c ƒ(x)? What can you say about the value of the limit at these points?
evauluate the limit lim x→0 (sin2 (3x))/ x2
1) Given limx→c f(x) = 3 and limx→c g(x) = 4, evaluate the limit:
Compute the limit:lim (1+3x)^(-5/x)x→0
- determine the limit lim_{h->0}[(x+h)2-x^2]/h by treating x as a constant. - determine the lim_{x->0} cos(2x)/x -determine the limit_{x->0} sin(2x^2)/xtan(4x) thanks...
Find limit of lim x-->0 of f(x)= (e3x-3x-1)/(4x^2)
Calculate the limit algebraically. (If an answer does not exist, enter DNE.) lim x→−2 x3 + 8 x2 + 7x + 10 If the limit does not exist, say why. (If the limit does exist, so state.) The limit does not exist because the left and right limits exist but are not the same finite value.The limit does not exist because only one of the left or right limits exists as a finite value. The limit does not exist because one side diverges to ∞ and the other side diverges to −∞.The limit does not exist because it diverges to ∞ or −∞.The limit does exist and is a finite number.