lim f(x) = 1 and lim f(x) = 0. * 3 * 3

Q: Sketch the graph of an example of a function f that satisfies all of the followingconditions:Range =…

A: It is given that, the range is [–2, 5] and the limit of the function are

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

A: the given limits are:

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

A: Given the function with the limits.

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: Sketch the graph of a function such that lim f(x) = -3,f(0) = 2, ƒ(2) = 5, and lim X-2 doos not…

A:

Q: In terms of limits, what does it mean for f to grow faster than g as x→∞? Choose the correct answer…

A: We need to choose correct option.

Q: 4. Are the two limits below the same? lim x-0 x| and lim x-0 X

A: As per our guidelines we are supposed to answer only one question i.e. the question no 4, which is…

Q: Let F(x) = (x2 + 3x + 2)/(2 - | x | ). Make tables of values of F at values of x that approach c =…

A: Given: Fx=x2+3x+22-x To determine: We have to estimate limx→-2Fx by making a table of values of F at…

Q: Give an example of a function that is not continuous at x = 2 but limx→2 f(x) = 1

A: choose any equation of line such that f(2)=1 but the function function f(x) should be discontinued…

Q: Give an example where lim (f(x) g(x)) exists but neither lim f(x) nor lim g(x) exists.

A: To give the examples  where limx→0f(x)g(x) exists but neitherlimx→0g(x)  nor limx→0g(x) exists.…

Q: 5. Consider the graph of f (x) shown. Does the lim f (x) exist? Is the function continuous at x=3?…

A: This question is related to limit and continuity,  we will solve it using given information.

Q: Sketch a possible graph of a function that satisfies the conditions below. (0) 0, lim f(x) - 1; lim…

A:

Q: 3. If f is a continuous function, what can you say about lim f(x)?

A: Given thatf is continuous To determinelimx→1f(x)

Q: Let g(x) = xe-* + be-*, where b is a positive constant. Find lim g(x).

A:

Q: Given that lim f(x) X+ 0 x2 1- explain why lim f(x)= ∞, x2 +7f(x)- sin (5x)+ 1 2- evaluate the limit…

A: We have to find the following

Q: Sketch the graph of the function and use it to determine the values of a for which limx--a f (x)…

A: We will find out the required values.

Q: Find a formula for a function f that satisfies the following conditions. lim fx) = 0, lim f(x) - -0,…

A: Function

Q: 5. If f(a) is undefined, then the lim S(x)does not exist. True or False? Explain.

A:

Q: Sketch the graph of a function f (x) that satisfies the following conditions: limx -→ -o f (x) = o ;…

A: Follow the steps to sketch the graph.

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. 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 -> 2,…

Q: lim F(x),

A:

Q: Is the function continuous at x = -3? If not, what type of discontinuity occurs? Explain. 6. lim…

A: Given query is find whether function is continuous or not on x =-3.

Q: Provide a diagram where limx→a f(x) exists, f(a) is not defined and f(x) is not continuous at a.…

A: A function f(x) has properties,limx→af(x) exits, f(a) is not definedfx is not continuous at x=a…

Q: Assume that –x4 < f(x) < x². What is lim f(x)? Is there enough in- formation to evaluate lim f(x)?…

A: Given: -x4≤fx≤x2 according to given data limx→0-x4=-04=-0=0limx→0x2=02=0 so, by sandwich theorem…

Q: Suppose that ƒ is an odd function of x. Does knowing that lim x--&gt;0+ ƒ(x) = 3 tell you anything…

A:

Q: Let f(x) = VT. Use the definition of derivatives as limit of difference quotient to show that…

A:

Q: If f and g are two functions such that lim f(x) as x --> a = + infinity and lim g(x) as x --> a = +…

A: Given: f &amp; g are two functions such that, To check if this statement is True or False

Q: Given the function f(x) = sqrt(x-2), please evaluate the limit. limx→∞ f(x)

A:

Q: Suppose that a function ƒ(x) is defined for all real values of x except x = c. Can anything be said…

A: Given: The function fx is defined for all real values of x except x=c, To determine: Whether the…

Q: 1. Evaluate lim f(x) if f(x) = {, if xs-1 &² - 2 if x>-1

A: Given function fx=1x,   if x≤-1x2-2 ,     if x&gt;-1 We have to find  limx→0 fx=?

Q: Let: cos² x +1 f(x) Determine: lim f(x), lim f(x), lim f(x). and X- Specify horizontal and vertical…

A:

Q: OUse the e, & definition of the limit to prove that: lim -4x + 5 = -3 x- 2 der: lim f(x) = L means:…

A:

Q: Calculate the limit.

A: limx→∞tan-11+x1-x

Q: Determine whether the statement is true or false. f(x)] If lim f(x) = 0 and lim g(x) = 0, then lim…

A: If limx→1f(x)=0 and limx→1g(x)=0 then limx→1 f(x)g(x)=limx→1 f'(x)g'(x).  This is L'Hospital's rule.…

Q: Use the graph to evaluate the limit. lim lim Find x-(-1) f(x) and X-(-1)+ f(x)

A: Consider the first given limit: This means that when x is approaching to -1 from left side then…

Q: Using the tabular approach, evaluate lim X-1+ Inx

A:

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

A: Given that suppose neither limx→0 f(x) exists nor limx→0 g(x) exists.Our Aim is to show thatlimx→0…

Q: Sketch the graph of any function that satisfies the following conditions: - f(3) = 2 - limx-->3-…

A:

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…

A: The graph of f is 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: Compulte limit ² lim Clnx)? X-X X-1

A:

Q: Sketch the graph of a function f such that: limf(x)=0 X-7

A: We take a function  f(x)= 1/(x-7)

Q: Give an example where lim 1x) x0 8(x) exists but neither lim f(x) nor lim g(x) exists.

A: Let us assume two functions Then,

Q: Sketch the graph of function f that satisfies all of the given conditions: lim f(x) = ∞, lim f(x) =…

A:

Q: Give a specific example of f(x) with limx→∞ f(x)=1 and limx→∞ g(x)=∞ such that limx→∞ f(x)^g(x)=0.…

A:

Q: Suppose that f is a function such that lim f(x) = 1, and that lim f(x) %3D %3D What is lim…

A:

Q: Assuming that lim x→a f(x)/(x−a)2 exists, find lim x→a f(x)/x-a

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.