- Determine the values of and so that the following function is continuous on the entire real line. Please use the definition of continuity studied in this chapter to explain why the values you found for b and c make f(r) continuous everywhere. I+1 f(x) = 12 + br +c a - 2|> 1

Q: 1. Determine all values of the constants a and b so that the following function is continuous for…

A: We need to find values of a and b.

Q: B) Test the functions continuity at the given poihts: (x²-x-6 1) f(x) 3D x * 3 ,at x 3, x 5 X-3 x =…

A: f(x)=x2-x-6x-3x≠35x=3

Q: For what values of a and b will f(x) be continuous on everywhere at x = 2 if the function is x2 – 4…

A: Given f(x) = x2-4x-2x<2ax2-bx+32≤x<32x-a+bx≥3 It is continuous if and only if limx→2-f(x) =…

Q: The function f(x) is defines as  f(x)=e^(-1/absolute value of x) if x do not equal to 0;         0…

A:

Q: Determine the domain of the function and prove that it is continuous on its domain using the Laws…

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Q: 3. Use the definition of continuity and the properties of limits to show that the function is…

A:

Q: What value should be assigned to c so that f(x)= the set of real numbers? x²+x-20 x-4 3c x < 4 x ≥4…

A: Given that fx=x2+x-20x-4x&lt;43cx≥4. The objective is to find the value of c.

Q: Given the function, g(x) 3 x 2 a. Determine the possible points of discontinuity. b. Discuss the…

A:

Q: If for a real continuous f(x), f(a) f(b) < 0, then in the range of [a,b] for f(x) = 0, there is…

A: It is given that f(x) is a continuous function and f(a)f(b)&lt;0. Then f(a) , f(b) have opposite…

Q: Give an example of functions ƒ and g, both continuous at x = 0, for which the composite ƒ ∘ g is…

A: A function is said to be continuous at any point a, if A composite function is defined as a…

Q: Find a value ofk such that the following function is continuous at all real numbers. 3x-4 if x1 If…

A: Let fx be the given function . Then f is continuous at x = a iflimx→afx = fa

Q: Consider the following function: - 4 if x 3 Find the values of a and b that make f continuous…

A: The function is continuous every where, if it is continuous at each point in the domain. The…

Q: Discuss the continuity of the following function: 2* (1- x), x0 x < 0 x = 0

A:

Q: x + 20 g(x) = { 3Cx + K if – 2 < x За — 2K if x < -2 | if 1 < x -

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 0 < x < 1 1 < x < 2 X = 3 3 < x <4 x = 5 2 - x , 3 Test continuity for the following function: F(x)…

A: Given: Fx=2-x,0≤x&lt;13,1≤x&lt;22,x=3-2x-2,3&lt;x≤40,x=5

Q: Use the definition of continuity and the properties of limits to show that the function is…

A: We have to use the definition of continuity and the properties of limits to show that the function…

Q: [4] Let k and c be real numbers. Let f(x) be a piecewise function defined by x + 3 if x 2 Using the…

A:

Q: 1. Determine all values of the constants a and b so that the following function is continuous for…

A:

Q: Use the definition to determine whether the following function is continuous and differentiable at x…

A:

Q: Find the value of that will make the function f(x) continuous everywhere. f(x) = {ka² -2, (4x+k,…

A: Given function is- f(x)=4x+kx≤-5kx2-2x&gt;-5 To find- To find the value of k that will make the…

Q: -x ifx1 function f. Where is f discontinuous? Justify your answer using the definition of…

A: We first make a table for the function x -4 -1 0 0.5 1 2 3 4 y 2 1 1 0.5 DNE 1 4 9 Then we…

Q: State the definition of continuity and then define P so that the function f is continuous at x =-2,…

A: Given function

Q: The function f(x) = (x² - 4)/(x-2) is continuous at x = 2. Select one: O True False The function…

A: Continuity of function

Q: find the values of the constants a and/or b needed to make the following functions continuous for…

A: To fix the values of the unknown a and b to ensure the continuity of the given function

Q: The function f(x) = 2/(x-5) is continuous on the interval (0, 5). Select one: O True O False The…

A: Answer: false

Q: 1. Determine all values of the constants a and b so that the following function is continuous for…

A: We have to find a and b

Q: B- If f(x) = is continuous at x = Find A? |Ax2 x2

A: The explanation of the answer as follows

Q: Does there exist a real number c that makes the following functions continuous over (−∞,∞)? If…

A: If function is continuous at point of given interval, then

Q: 1.βx − 3 if x ≤ 2(b) Suppose that f(x) = βx + 2 if x &gt; 2Find the value of β so that f(x) is…

A: For continuity, left hand limit=right hand limit=f(x)

Q: O Find a value for A such that the function f is continuous at all real numbers: if x 3

A: For continous function L.H.L=R.H.L=fxNow find…

Q: (d) The function k(x)is defined as follow: 3 x+ 17 -- 4 k(x) = { 2, x =1 5|x-1| x² -1 x>1 Discuss…

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Q: Discuss the continuity of the following function: (2* (1– x), x 0 x = 0

A: Consider the given:

Q: x' - 27 x² -9 (c) at x = 3 and x = -3

A: First of all to find critical points put the denominator equal to zero. x2 - 9 = 0 x 2 = 9 x = 3, -3…

Q: 3. Determine the values of a and b so that the following function is continuous on (-00,00) ax+b if…

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Q: Find all possible (real number) values of p, q, and r, if any, which result in the following…

A: Given, f(x)=x2-px+6if x&lt;-6px2+x+qif -6≤x≤-4sin(x+4)9(x+4)+qx+rif x&gt;-4

Q: SBx? - з (Bx + 2 if Suppose that f(x) = x > 2 if Find the value of ß so that f(x) is continuous…

A: For continuity, left hand limit=right hand limit=f(x)

Q: 3. Use the definition of continuity and the properties of limits to show that the function is…

A: As per our guidelines we are supposed to answer only one question i.e. the question no (a). For the…

Q: (kx – 1 ifx< 2 G(x) = kx? 2. if x 2 2

A: the given function,   G(x)=kx-1if x≤2kx2if x≥2

Q: f(x) to 2. 2.

A:

Q: 3. Consider the function h whose graph is given below. a. Is h continuous at 1 = 0? Justify your…

A: Given,

Q: Find the values of a and b that make f continuous everywhere. x² - 4 X - 2 ax? - bx + 3 2х — а + b…

A: The given function f(x) is continuous everywhere, thus the function is continuous at x = 2 and x =…

Q: Determine the continuity and, if discontinous, the type of discontinuity for the function…

A: Given query is to find function is continuous or not at x = -1.

Q: Check the continuity of the following function at x = 1 (1+x f(x) =x (2-x if x <-1 if -1sx<1 if x21

A: Check for left hand limit and right hand limit and check whether they are equal or not.

Q: 4] Let k and c be real numbers. Let f(x) be a piecewise function defined by x + 3 if x 2 Using the…

A:

Q: (г? + 4х — 21) Let f(x) = for x + 3. How should f(3) be defined so that f will be continuous (л — 3)…

A:

Q: Find the values of a and b so that the following function is continuous on the real line (-inf, inf)…

A:

Q: Y 4- y = f'(x) 3 -3 -1 (1,0) 2 3 -4 (-3,0) W (0,-0.5) (2,-0.5) (3,-2) -1,-2) -3- (-1,-3) (4, -3) 2 I

A: Observe the graph and answer the question.  Concept:  h'(x) = 0  : h(x) has local maxima Or minima…

Q: 5. Which of the following is true for f(x) = x² -4 ? X-2 There is a non-removable discontinuity at x…

A: As we know that; A polynomial function y=fxgx is continuous everywhere except such x where gx=0.

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.