The greatest integer function, also known as the floor function, isdefined by [ x ] = n, where n is the unique integer such that n < x < n + 1.Sketch the graph of y = [ x ] . Calculate for c an integer:(a) lim [ x ]       (b) lim [ x ]       ( c) lim [ x ] x→ c               x→ c+                       x→ 2.6

Q: Use the graph of the greatest integer function, y = [x], to find the limits given below. Ay 4- [0]…

A: [.] the greatest integer function returns the closest integer less than or equal to the given…

Q: The graph of   f(x) = 2x2/(x2 + 2) is shown.…

A:

Q: The initial substitution of x = a yields the form Simplify the function algebraically, or use a…

A: Given: limx→32x2+5x-33x2-9

Q: Find the limit algebraically. ( f(-3 + h) – f(-3) lim h0 where f(x) = -3x2 + 2x + 9

A: Our objective is to find the limit algebraically.

Q: Find the limits a) lim x2 - 4x + 3 x2 - 1 when x approaches 1 b) lim 6x + 100 7x2 100 when x…

A: We have to find the limit

Q: Evaluate the limit for the graph: lim f(x). x-1- a) 2 b) 0 с) — 2 d) –o -00

A: -2

Q: (a) Use a graph of f(x) = V 2x2 + 9x + 5 – V 2x² + 2x + 2 to estimate the value of lim f(x) to one…

A: Here we have the find the limit of the function using a graph, table, and exact evalution.

Q: For the function graphed here, show that

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Q: Find the limit L.

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

A: the given limits are:

Q: Consider the graph of y = f(x). 4- -8 -7 -6 -5 -4 -3 -2 -1O 2 3 5 -2 For infinite limits, use 00 = 0…

A: As per our guidelines we are supposed to answer only first three parts. kindly repost others part as…

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 1 1 lim x 8 X - 8

A: To evaluate the limit of the function given.

Q: Sketch the graph of the given piecewise function and determine the following limits x2+1, x>2 f (x)…

A:

Q: Use numerical or graphical evidence to determine the left and right hand limits of the function. |7x…

A: find the limit of function, using graphical or numerical method. from the solution, we can say that…

Q: Find the limt lim e - x メ→の e-メ

A: Evaluate the limit  limx→∞ ex-x2ex-x

Q: Use a graph of f(x) = In x to answer the following questions. (a) Find lim In x. (b) Where does the…

A: WE have to use the graph of f(x)=ln(x) to find , a) limx→0+f(x) b) where does the function ln x have…

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

A:

Q: Consider the function g graphed below. x+3, for x < - 2 g(x) = . 5x-2, for x -2 8- 4- Find lim (x).…

A: Given that,           g(x) = x + 3         for x &lt; -2                     - x/2 - 2      for x…

Q: 1. (a) Use the graph below to estimate the following: lim f (x)=, x2 8 = when &=1 (b) Label a, L, ɛ…

A:

Q: If a function is defined at a, but lim f(x) does not exist, how is x→a this shown on the function's…

A: If the limit of a function f(x) does not exist at a, then the function is not continuous at a and…

Q: Estimate the value of lim 1 + 3x 1 by graphing the function f(x) = x/(/I + 3x – 1).

A: It is given that limx→0x1+3x-1 It is known that if we have limx→af(x)g(x), and after plugging the…

Q: 1. Decide whether the function f(r) = admits any horizontal asymptotes, i.e. compute lim f(x) = Give…

A: (1). The function is given by f(x) = xx+4 To evaluate : The horizontal asymptote.

Q: Find the limit. (a) lim 1- 2x 3 *-2 (b) lim (c) lim .2 3. - X . /レ r o X +x

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: draw the graph of a function on [0, 5] with the given properties.

A: Removable discontinuity at any point (a) of domain of function (say f(x)) is define as Graphically…

Q: Use the graph to estimate the specified limit. lim f(x) and x-47/2) lim f(x) x-47/2)* Find

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Q: In a model of the nervous system, the intensity of excitation of a nerve pathway is given by I = E[1…

A: Given  that: I=E1-e-a(S-h)E

Q: Find the limit L.

A: limx→23x+2

Q: Calculate the limit algebraically: x³ + 8 lim x→-2 x² + 7x + 10

A: Consider the given expression, If we substitute  in the expression we get  form. so, use L-hospital…

Q: lim (In 2x + 5) + 4 X→ー1

A: Solution:limx→-1ln2x+5+4=ln2-1+5+4

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim x→10+ 10 − x x2 − 100

A: To Find: limx→10+10-xx2-100 Concept: i. limx→a+fx=limh→0fa+hii. x2-a2=x-ax+a

Q: lim (-2 xS t x-1)

A: From this limit, we know that when x approaches -infinity then y approaches +infinity. so, on the…

Q: Find the limit. 4) lim (e5/x - 6x)\/2 x-0+

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Q: evaluate the limit.

A:

Q: Evaluate the limit. lim I-+0 V1+ 9x – 1

A: To evaluate:  limx→0x1+9x-1 if we substitute x=0 in the limit we get x1+9x-1=01+0-1=00    undefined…

Q: 1. Use a table of values to estimate the limit correctly to the nearest hundredth. x' - 3x? +2x –- 6…

A: Please see the answer below.

Q: lim(-3x² – 1) x-3

A: Solution:

Q: Use the graph to estimate the specified limit. Find lim f(x) and x-(7/2)" f(x) lim x-(7/2)* 2 -11…

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Q: B. If k is any real number, prove or disprove that sinkx 1. lim x-0 kx = 1.

A: We will prove this by L'Hopital's rule

Q: 2. Let b be the brightness of a light source, and A be the area of a human’s pupil. Suppose that…

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Q: Use the graph to compute the quantities asked for. a. lim f(x) b. lim f(x) I-1 1 a) -2 b) -1

A: To find the limits

Q: Find the limit. x* – 1 - lim x→0+ In (x) +x – 1 п lim ( 1+ n

A: These question is based on Limits.

Q: Evaluate the limit L, given lim f(x) = -12 and lim g(x) = 3 %3D %3D lim [f(x) + 3g(x)] L = 1.

A: Solving by limit property

Q: A graphing calculator is recommended. For the limit lim (x - 4x + 5) = 20 illustrate the definition…

A: Consider the limit: limx→3x3-4x+5=20  Find the largest possible values of δ corresponding to ε=0.2…

Q: Use the graph to estimate the specified limit. lim f(x) and x-(n/2) 25) Find lim f(x) x-(n/2)* 2n

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Q: Find the limit. a(x + h)³ – ax³ lim h

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Q: 2. a. Draw a graph with the following characteristics: lim f(x) = 3 X->2* lim f(x) = 0 %3D x-→2 f(2)…

A: The graph has the properties,limx→2+f(x)=3limx→2-f(x)=0f(2)=3limx→-1f(x)=-2f(-1)=1

Q: What exactly does lim

A: Definition of the limit: Consider f(x) be any function that is defined on the the open interval…

Q: 12. Find the value of the limit: lim a. +00 b. -00 d. Indeterminate

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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.