The floor function For any real number x, the floor function (UI greatest integer function) [x] is the greatest integer less than or equal to x (see figure). a. Compute lim [x], lim [x], lim x], and lim [x]. x→-1 x→-1

Q: 1. Evalaute lim ƒ(x), lim ƒ(x), lim f(x) for I-3+ 2-3- 1-3 f(x)= { = −x+4 x − 3 x 3

A: Topic = Limits As per guidelines , At a time only one question with three sub-parts can be answered…

Q: 2. Find a formula for f that satisfies the following conditions: lim00 f(x) lim-3- f(x) = 0, 0,…

A: Rational function –          In a rational function we have to find intercepts, asymptotes and end…

Q: 57. Find a formula for a function ƒ that satisfies the following conditions: lim f(x) = 0, lim f(x)…

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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: The graph of a function f is shown in the figure above. Which of the following limf(x) = 1 %3D o lim…

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Q: 1 if x is an integer Let f be the function defined by f(x) = { oif x is not an integer a.) Sketch…

A: The given function,f(x)=1if x is an integer0if x is not an integer

Q: Using the graph of f(x) given below lim f(x) x→2 O 2 O 1.5 O 1 does not exists I|

A: Given graph of f(x)  we find x→2lim f(x)

Q: 1. Find the limit L. Then use the e-8 definition of limit to prove that the limit is L. lim 3x-1 x-4

A: Given, The limit

Q: 2. Consider the function F, that assigns x in its domain to x²-1 F(x)= |x-1| In its domain. a. What…

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Q: Find the value of the postive constant c, such that  lim x->infinty ((x-c)/(x+c))^x=1/4

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Q: 61. Let f(x) = x/x for x > 0. (a) Calculate lim f(x) and lim f(x). (b) Find the maximum value of f…

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Q: A) -1 ind the limit, if it exists. x2 - 16 if x>0 X + 4 12) Let f(x) = %3D x2 - 16 if x<0 x - 4 Find…

A: SOLUTION-

Q: The greatest integer function, also known as the floor function, is defined by [x] = n, where n is…

A: y=x is the greatest integer function.

Q: 7. Prove: if lim,+ f(x) = L, and lim₂+ g(x) = M, then lim f(x) · g(x) = LM. DE-I

A: To provide: A counterexample of the statement: If limx→af(x)=L and limx→ag(x)=M Then,…

Q: 8 Given a function: f(x) = (х-7)(х-1) Write down the definition that lim f (x) = L 8 OProve that lim…

A: Substitute x= 5 in the function and find the limit

Q: a/Limit of a function Lim A = 0 B = 1 O 3 €3¾/1 x²+2x-1 X 3+3X² 3

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Q: c) Fill in a table of values for a function h(x) that would satisfy lim h(x) = 1 and lim h(x) = 10.…

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Q: The table gives the values of g near 3, but not equal to g. Use the table to estimate lim g(x) = X-3…

A: The given table is,

Q: the graph of an example of a functionf that satisfies all of the given conditions. 15.) lim f(x) =…

A: We have to solve given problems: We

Q: 7. If lim f(x) =∞, lim f(x) = 3, and lim f(x) = 0, what X-00 x1+ can you say about any horizontal…

A: If limx→∞fx=L Then,              y=L is a horizontal asymptotes of f.   Here, it is given…

Q: (a) Use a graph of f(x) = V 3x2 + 8x + 3 - V 3x2 + 3x + 2 to estimate the value of lim f(x) to one…

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Q: Choose the best answer for limit.

A: limx→2-f(x)=limx→2-f(x)=-1 , f(2)=1we have to find limx→2f(x)

Q: 3. Define the function f(x) (a) Evaluate lim f(x) x →0+ (b) Evaluate lim f(x) x-1 = 2x n+m m x & Q m…

A: Here we use the way of function definition. And use the definition of limit of function at a point…

Q: If lim f(x) = L and lim f(x) = M, where L and M are finite real numbers, then what must be true…

A: Given that limfxx→a-=L snd limfxx→a+=mwhere L and M are finite real numbers ,then we have to find…

Q: b) The function g is defined by 4 x-2 x+2 Show that lim g(x) exist. X -2

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Q: f x^n / e^x =__

A: lim as x goes to infinity of x^n / e^x = 0

Q: 1. Using the graph of f(x), what is lim, -f(x)? A. - 00 B. 0 C. -2 D. Does not exist E. 00 A

A: The graph of f(x) is represented by two infinite curves.

Q: Let f, g and h be functions defined on R \ {0} such that both f and h are even functions, g is an…

A: f and h are even function and g is an odd function

Q: 1. Using tables of values, determine the limits of the following. (a) lim (a) (b) lim)2x) (c) lim…

A: At any point a the limit limx→afx=L exists if LHL=RHL=fa. The left hand limit LHL and right hand…

Q: 1. Evaluate the limit if it exists: lim x2+x-6 x> 2 2х а. 5 с. -3 lim v(x-5)-2 b. 3 d. -5 e. DNE 2.…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 39. The greatest integer function, also known as the floor function, is defined by [x] = n, where n…

A: a) Given, c=integer c- means less than c,  So integer before c- is = (c-1)  So, Answer(a): c-1

Q: Using the graph of f(x) given below lim f(x) = x→2 O 2 O 1.5 1 does not exists

A: Graph of the function is given, we have to find the value of limit at x=2

Q: Sketch the graph of a function f(x) that satisfies all of the following properties. limx__)…

A: Based on the given information, we can draw the following conclusions: 1) The lines y=-4 and y=3 are…

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

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Q: (a). Determine the interval(s) on which f(x) = is continuous. (b). Find lim analytically. 9-1 3 -1…

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Q: (a) Estimate the value of lim x2 + x + 7 + x→ -の by graphing the function f(x) = x + 7 + x. (Round…

A: Here we have to estimate the value of the given limit of f(x) .      f(x) = √(x2+x+7) + x

Q: (a) Estimate the value of lim X - -00 (V x2 + x + 7 + x by graphing the function f(x) = V x2 + x + 7…

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Q: The greatest integer function, also known as the floor function, isdefined by [ x ] = n, where n is…

A: Consider the given function, y=x draw the table of points, x y 0&lt;x&lt;1 0 1&lt;x&lt;2 1…

Q: x-1 ,when x=2,1.5,1.1,1.01,1.001,1.0001,0, 0.5,0.9, x' -1 Q.1. Make a guess about the lim: x->I…

A: Given: limx→1- x-1x3-1 We find the values of x-1x3-1for the given x values.

Q: 2. Suppose f is a positive function. If lim,»a f(x) = 0 and lim, a g(x) = 0, show that lim [f(x)]•w…

A: limx→afx=0  &amp;  limx→agx=∞

Q: 3. The function f is defined for all real n umbers except for x = -3. What is a reasonable estimate…

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Q: 4. Sketch a function f such that: lim f(x) and f(4) exist and are equal to one another. x→4 5.…

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Q: (a) Use a graph of              ______________       ______________f(x) = √3 x2 + 8x + 6  -  √3 x2 +…

A: From the graph, the value of  f(x) to one decimal place islimx→∞ 3x2 + 8x + 6 - 3x2 + 3x + 1 ≈ 1.4

Q: valuate the limit, if it exists. (If an answer does not exist, enter DNE.) lim x→−3  x2 + 3x/x2 − 4x…

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Q: 1. (a) Find the interval in which conditions of Rolle's theorem are satisfied for the function f(x)…

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Q: Evaluste the indicated limit by evaluating the function-for values shown in the table and observing…

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Q: lim, x – 1 x→-∞ p² +1 - -00

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Q: 1. Consider the function f (x) = {-x – 6, x 0 %3D Use table of values to find the limit of the…

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Q: With lim f (x) = +o and lim h(x) = -∞ for any a that x→a' x→a is real number, which of the ff. is…

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Q: Considering the definition of f(x) below, find lim f(x). -22 +x+1 if x 5 Select the correct answer…

A: Solution: The objective is to find the value of the given limit

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.