4. Is it possible that there exists some function g(x) and some constant L such that lim g(x) = lim g(x) = L, but lim g(x) does not exist? If so, draw a sketch of such a x-2+ x-2 function. If no, explain why not.

Q: 3. If lim f(x) = 5 and lim f(x) = 5, what can you say about x1 X1+ lim f(x)? What can you say about…

A: Definition used -       Limit of a function -       The limit of a function at point x=a…

Q: 7ーズ 1. Find lim using a. Table of values f(x) b. Limit rules

A:

Q: (-금x+ 2, x 0 exist? If yes, give its value. If not, why?

A:

Q: 7. If you know in advance that lim f (x) exists, can you determine its x→5 value just knowing the…

A:

Q: sketch the graph of a function with the given limits.

A: the given limits are:

Q: Determine whether the statement makes sense or does not make sense, and explain your reasoning.

A: Consider two functions fx & gx By algebra of limits, we have, 1. limx→a fx+limx→a gx=limx→a…

Q: 43. Assuming that lim 4 = 1, which of the following statements is necessarily true? Why? (a) f(0) =…

A: Consider a f0=0Here if x=0 , f0=0Substituting in limx→0fxx=00Inderterminant formDifferentiate…

Q: Evaluate lim f(x), where f(x) = e value of "p" assuming that lim f(x) exists. Nx + (M + 77) if x<5…

A:

Q: Sketch the graph of a function with the given limits.

A: Given the function with the limits.

Q: Prove using formal definition. (a) lim x→0+ 1/x = ∞.

A: Draw the graph of the function .

Q: Suppose that on the interval (2,5) f(x) less than or equal to g (x) less or equal to h (x) and Lim…

A: We have the following information.

Q: Find two functions f and g such that lim f(x) and lim g(x) do not exist, but lim [f(x) + g(x)] * 0…

A:

Q: Let f(x) = x/(x + 1). What is lim, »f(x)? How large does x have to be so that f(x) > 0.99?

A: Given:            fx=xx+1 Find: limx→∞fx=limx→∞xx+1

Q: lim 극 et – 1 x-1

A:

Q: a. Find the Domain for y = = /4 -x + ! b. For what value of (k) is the function y-f(x) continuous at…

A:

Q: If you know in advance that lim f (x) exists, can you determine its X+5 value from a plot of ƒ for…

A: Given that limit of f(x) exists at x=5.That means the function f(x) is continuous and differentiable…

Q: If lim f(x)=-2 and lim g(x) = 2, what is the value of lim [f (x)+2g(x)]?

A: Given, limx→afx=-2  and  limx→agx=2

Q: Show that if lim f(x) = lim h(x) = 3, and if f(x) ≤ g(x) ≤h(x) for 2-0 x-0 all z € (-1,1), then lim…

A: Given that limx→0fx=limx→0hx=3 and fx≤gx≤hx for all x∈−1,1. We have to prove that limx→0gx=3.…

Q: 3. Find the indicated limits. if x 2 f(x) -2+ 4x – x² a) lim f(x) x→2+ b) lim f(x) x→2- c) lim f…

A:

Q: Suppose that a function f(x) is defined for all real values of x except at r = c. Does it imply the…

A: Here we have to check whether the limit exists or not.

Q: what is the lim f(x)9(x) if lim g(x) ln f(x) = +∞ x→a x→a

A:

Q: [3 3. Consider f (x) =- 2х - 3 if x< 0 Find lim f(x) if x20.

A: To determine the limit of the function.

Q: 4-If. 2-x < f(x) < 2Cos(x) for all x then find: lim f(x)

A: I applied sandwich theorem which is defined as

Q: 5. If lim f(x) = 8 but lim f(x) does not exist, what can you X+2+ X+2 say about lim f(x)? X2-

A: We know that, limx→afx=l, if: limx→a+fx=limx→a-fx=l

Q: Give examples of functions f(x) and g(x) with limx→∞ f(x) = ∞ and limx→∞ g(x) = 0

A: We want to find two functions f(x) and g(x).

Q: 1/x, if x – 1 С. 1/x, if x – 1[ %3D X- -1

A: c) f(x) = 1/xx≤-1x2-2x&gt;-1limx→0f(x) = limx→0(x2-2) = 02-2 = 0-2 = -2

Q: 1. Determine the lim f(x) if f(x) : = {x*. if #2 lo, if x = 2 2. Find lim f(x) if f (x) = 2*

A: (1) Given that, f(x) = x2 ; if x is not equal to 2 f(x) = 0 ; if x = 2 Then we get, As x -&gt; 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: Determine whether the statement makes sense or does not make sense, and explain your reasoning.

A: lim x→4fx = 0lim x→4gx = 0To verify:          lim x→4fxgx ≠ 0   is correct or not.

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: Consider a function x-1 if x 1 (a) Find lim f (x) if it exists. If it doesn't exist, explain why.…

A:

Q: 1. Using L'Hospital's rule, evaluate lim(1 – x²).

A:

Q: 3 - – If lim f(x) = 3.5 and lim,-2+ f(x) = 6. 5 , the function has a double sided %3D x→2- limit or…

A: Given,          limx→2-fx=3.5 and limx→2+fx=6.5We know that,           Condition of double sided…

Q: lim f(x)=+0, then the limit lim [2² . f(x)] .. If must be equal to zero. must be equal to +00. must…

A:

Q: (3х + 3с if x >2 Let f(x) = {x2 - cx if x < 2 If lim f (x) exists, find the value of c. X-2

A: Limit of a function exist , when both sided LHL and RHL exist.

Q: 1. Sketch a graph of a function f(x) with the following properties: f(-2) = 0, ƒ(2) = 0, lim_f(x) =…

A:

Q: 6. Given f(x)= { 3, if x < -2    x, if -2 ≤ x<8    x+3, if x≥8  estimate lim f(x) x→−2     a.-2…

A:

Q: Evaluate lim (e* – 2.x) x→0-

A: To evaluate: limx→0-(e3x-2x)3x

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…

A:

Q: 3. Show algebraically that lim x* – 2 – x = 0

A:

Q: 1) If lim f(x) = , what asymptotic behavior will be illustrated in the graph of f (x)?

A: 1) If limx→6-fx=∞, then the value of the function fx tends to infinity as x→6 from the left hand…

Q: Suppose that f (x) is a function such that lim f(r) and lim f (r) both exist. Does this mean lim…

A:

Q: Consider the function - x2, x+1 f(x) = 2, x = 1 O Graph the function f(x). O Find lim,1-f(x) and…

A:

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: Investigate the one-sided limits graphically: (a) lim x→2# x – 2 (b) lim x→0± x2 (c) lim In x x→0+

A:

Q: What type of discontinuity is at x = 3, if lim f (x)= 0 and lim f (x)= 0? x-3 x>3* What type of…

A:

Q: Suppose that g(x) < f(x) < h(x) for all x 2 and suppose that lim g(x) = lim h(x) = -5. Can we…

A:

Q: Suppose g(x) is a function. sin(32) If lim 9(x)+ =8, then what is lim g(x) ? Your answer should be…

A:

Q: ,if x> -3 Given the function f(x) =' 3 ,ifx S-3 is continuous at x=-3

A: A function                      fx=x2-9x+3,   if x&lt;-33,             if x≤-3 We have to answer the…

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.