Let if x<0 f(x) = {3 – x if 0 3 - (a) Evaluate each limit, if it exists. (i) lim f(x) (ii) lim f(x) (iii) lim f(x) (iv) lim f(x) x3- (v) lim f(x) x3+ (vi) lim f(x) (b) Where is f discontinuous? (c) Sketch the graph of f.

Q: The graph of a function f for which f(2) does not exist but lim f(x) x-->2 does exist. create an…

A:

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

A:

Q: x2 Evaluate the limit: lim 3x – 40 - - x →8 x – 8

A:

Q: lim (x² + 4x) 2. X→-4

A:

Q: Sketch the graphs of functions that have the given limits and values. lim f(x)= infinity x-->2-, lim…

A: Given limits for the function is limx→2-fx=∞ ,  limx→2+fx=-∞ That is when x approaches 2 from left…

Q: Use properties of limits and algebraic methods to find the limit, if it exists. (15– 2x for x<7…

A:

Q: Evaluate lim x->-1 if f(x) {  1/x if x < -1                          { x2 - 2 if x ≥ -1

A: To evaluate: The limit limx→-1fx. Given: The function is fx=1x,        If x&lt;-1x2-2    If x≥-1.…

Q: find the limit.  lim(x-->2^-)    ln(-1/x-2)

A: Here we have to find the left hand limit at x = 2.

Q: lim X+2 X- 3 X-2

A: "Since you have asked multiple questions. We will solve the first question for you. If you want any…

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

A: WE HAVE TO FIND THE VALUE OF THE GIVEN LIMIT    THE GIVEN EXPRESSION IS limx→∞2+x2-x

Q: Evaluate the limit limx>infinity x2e-x

A: Consider the given limit limx→∞x2·e-x

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: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

A: If we could show that the LHL of 2 and RHL of 2 and f(2) are equal then the limit ate x=2 exists.…

Q: 7. Evaluate the limit: 9x2- 2 lim 2 2-3x 8. Evaluate the limit: 1-5x2 lim X0x2-x4 9. Evaluate the…

A: We are entitled to answer three sub-parts. Please resubmit the question which you wish to get…

Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

A: Givenf(x)=9-2x   , if x&lt;3x2-x    , if x≥3

Q: Find the limit when x-> 0 lim(√x+11-√11)/x

A:

Q: Use continuity to evaluate the limit. lim x→5 x   29 − x2

A: We have to determine  limit use continuity

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: а. If lim f(x) and lim f(x) exist, then so does lim f(x). 2at For those who have trouble viewing the…

A: To determine whether the given statement is true or false

Q: Prove that limx-&gt;∞ f(x) =lim t-&gt;0+ f(1/t) and  limx-&gt;∞ f(x) =lim t-&gt;0- f(1/t)   if these…

A: We have to prove limx→∞fx=limt→0+f1t Take limx→∞fx Put t=1x when x→∞ then t→0 we get…

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: Find the limit (if it exists) or show that the limit does not exist lim(x,y)-->(0,0)  x2+y2/x2-6y2

A: Here, we will show that the limit of limx, y→0, 0x2+y2x2-6y2  doesn't exists. Along x=0:…

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…

A:

Q: 4. If lim f(x) = -2, lim f(x) = 3, and f(0) = -2, what can X0+ X0- you say about lim f(x)?

A: Given, limx→0+f(x)=-2limx→0-f(x)=3f(0)=-2     Find limx→0f(x)

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 properties of limits and algebraic methods to find the limit, if it exists. x² - 81 lim x--9 x +…

A:

Q: 4-V3x+1 Evaluate the limit limx→5 x²-7x+10

A: Given limitlimx→5 4-3x+1x2-7x+10

Q: Evaluate the limit: lim t---->0 e2t - 1 / et -1

A:

Q: • Find the limits of 2+x-V2 • lim Vx -3 • lim X→9 x-9 x³+1 lim X--1 x+1 V5+x -V5-x • lim x-0…

A:

Q: Use properties of limits and algebraic methods to find the limit, if it exists. x2 - 81 lim X -9 X +…

A:

Q: find the limit of lim x->3 sin(x-3)/x^2-x-6

A: To find limx→3sinx-3x2-x-6

Q: Evaluate the limit lim (x=2^+) = 1/x-2

A:

Q: Find the limit.  lim x--> infinity  ln (3x2-1/x2+1)

A:

Q: -x - 4, x 3

A:

Q: Find the limit. x-x lim x→11- Vx х-х* lim x→11- Vx (Type an integer or a simplified fraction.)

A:

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

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: lim_(x→-inf)((1-2x)/3x) Find the limit and show proof

A: The limit of even function is given as follows :

Q: True or false: For lim f(x) x--> c to be defined, the function f must be defined at x=c

A: Solution The objective is determine whether the given statement is true or false

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

A:

Q: 5. Find the limit of lim x* +0-x

A: Topic = Limits

Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

A: For existance of limit,  lim f(x)x→a- =  lim f(x)x→a+

Q: 1. Shows that the function f(x): x2+2 Lis continuous at x = 0, but has jump discontinuity at x-3 x=…

A: 1. f(x)=x2+2x-32. f(x)=x2-9x-33. limx→-12x2-ax-14x2-2x-34. f(x)=x2-xx-1

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…

A:

Q: 4-x lim x→4 5- Vx2+9 a) Evaluate the limit

A: When we get indeterminate form , we use L'Hospital rule i.e. differentiating numerator and…

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.