23-24 How would you “remove the discontinuity" of f ? In other words, how would you define f(2) in order to make f continuous at 2? x3 24. f(x) 8 x? – 4

Q: 1. (Find the value of a so that the function f(x) is continuous everywhere.f(x) ={2x+a if x<1…

A: Given:

Q: 5а — 2 if x 10 If f(x) is a function which is continuous everywhere, then we must have b :

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Q: —с — 2 if x 2 с — 3 if A h has a removable discontinuity at x=2. В h has an essential discontinuity…

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Q: 6x -4, xS 5 -kx + 6, If the function f (x) = is continuous at r = 5, then the value of k is --- --…

A: The given function is: This function is continuous at x = 5, if at this point left side limit,…

Q: Question 29

A: It is known that, the domain of the function is set of all set of all possible values of x for which…

Q: (12|+ 3, if xs-3 Let f(x) ={ -2r, if -3 <x < 3 6r +2, if x2 3. Show that f(x) is continuous at x =…

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Q: #26

A: 26. The given function is,

Q: тӕ 11 if x - 4 If f(x) is a function which is continuous everywhere, then we must have = u

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Q: - 7 f(x) (x – 2)(x +1) is continuous. f is continuous on

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Q: 1- 10 Consider the function defined by (x3 -3 f(x) = {? +1 if x 2 Is it continuous at x = 2?…

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Q: Consider the following. X + 5 x2 f(x) - X - 3O Find the x-value (if any) at which f is not…

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Q: Example 1: The function has a removable discontinuity at 2. How would you redefine f(2) to make f…

A: Given: also, this function has a removable discontinuity at 2.   To determine: redefine f(2) to…

Q: hich of the following is a function that has a jump discontinuity at z = 2 and a removable…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 5. The function f(x) is defined as: 4x3 +17x2 + 13x +36 x -4 ontinuous for all values of x. What…

A: solution:-f(x)=4x3+17x2+13x+36x+4     x&lt;-45x2+2x+a                       x≥-4f(x) is continuous…

Q: How would you "remove the discontinuity" of f? In other words, how would you define f(4) in order to…

A: Discontinuity of f can be removed by factorisation of the numerator

Q: Question 26

A: To determine the domian of the function.

Q: 4- if f(x)= {† * *S S2 +x x 15 is this function is continuous or dicontinuous a) continuous b)…

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: 3-64 -If f(x)=04 is the function continuous at x=4 x-4

A: If a function f(x) is given and we have to check continuity at x=a then we have to find LHL, RHL and…

Q: 8. A restriction on the domain of f(x)=x²-9, so that f-¹(x) is also a function, could be 0-3≤x≤3…

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Q: 2. Let f(x)=1- x2/3. Show that f(-1)= f(1) but there is no number e in (-1, 1) such that f'(c)= 0.…

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Q: Suppose that f(x) = 2 for x &lt; 3 and f(x) = -4 for x &gt; 3. (a) What is f (3) if f is…

A: For x&lt;3,f(x) = 2For x&gt;3,f(x) =-4Part (a) - f(3) = ? when f(x) is left continuous.f(3) =…

Q: 5. Suppose f(x) is an odd function. Prove that g(x)=f(x)| is an even function.

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Q: 5. If f(x)=3*-9 and g(x)= tanx, then what is the domain of (g+f)(x) on the interval [0,2m]?

A: For the given question, we can write the function (f÷g)(x) as:f(x)g(x)=tanx3x-32Hence, the domain of…

Q: 7. Find the value of the constant k such that the foloowing function is continuous for all values of…

A: Take LHL=RHL

Q: 3. Determine whether the function is continuous at r = 5. 2²-42-5 2-5 x 5 D

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Q: 1. Determine where each of the following functions are continuous. x2 - 3x - 10 a. f(x) = %3D x2 -…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: See picture below. Can you please show me the steps to solve this?

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Q: 9. If f (x) = prove that f (xr) is an even function. et -1 2

A: A function f(x) is said to be even if we have f(-x)=f(x)

Q: 1. Find the x-values (if any) at which f is not continuous. Which of the discontinuities are…

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Q: x+4 if x3 Is it possible to defined f at x=-2 in such a way that f becomes continuous at x=-2? If…

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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: Consider the function f with domain (-2, : 3|22 – 1| if – 2 < x < 1 2x2 + 2x – 4 f(x) = 3 if x = 1…

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Q: - We define the function f: R -> R as follows. Let f(x) = x-2 for X2, and f(x) = a for x=2. What…

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Q: What can be said about f (3) if f is continuous andlim f(x) = ½? x→ 3

A: Given that, the function f(x) is continuous and limx→3fx=12. Since, function f(x) is continuous in…

Q: Is it possible to determine f(7) if f(x) = 3 for all x &lt; 7 and f is rightcontinuous at x = 7?…

A: Solution: Consider the given that f(x) = 3 for all x &lt; 7 f is right continuous at x = 7  The…

Q: Only question 21Explain why the function is discontinuous at the given number a. Sketch the graph of…

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Q: 2- 62 Suppose that f is a function given by { |x+ 5| x1/5 if x 32. (a) At which x-values does f not…

A: Topic :- Functions

Q: x + 4 if x 3 Let f(x) = (10 – 2x Is it possible to define f at x = 1 in such a way that f'becomes…

A: if f(x) is continuous at x=1 then  limx→1-f(x)=limx→1+f(x)limx→1-f(x)=-x=-1

Q: x2 – 1 - 1 x 2

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Q: 1. Determine whether these statements are always true or sometimes false. (a) The function f(x) |a-3…

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

Q: - 10 тх — 12 x2 + 3x – 2 if x > if x < Let f(x) = -10 If f(x) is a function which is continuous…

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Q: 2. Find the value of k so that the function defined ( x2 + 4 x 2 - x = 2.

A: A function is a relation which maps each value in its domain to exactly one value in its range.…

Q: If f is differentiable and f'(x)=x³-2x²-x+2, then fis increasing or

A: Given, x³−2x²−x+2=f' We equate the given function to zero for critical points. x³−2x²−x+2=0   Step…

Q: * - 36 Define g(- 6) in a way that extends g(x) = to be continuous at x= - 6. x + 8x + 12 g(- 6) =|

A: topic - limits

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

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Q: Suppose f(x) is differentiable everywhere and f(-3) Show f(1) > -6 and f(-5) -2.

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Q: How would you "remove the discontinuity" of f? In other words, how would you define f(3) in order to…

A: Given, fx = x2-2x-3x-3  We have to define f3 in order to make f is continuous at 3.

Q: Q12: Discuss the continuity of function f(x) at x-3 x²-9 if x # 3 6 if x = 3 F(x) = {x-3 %3D

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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.

Q: 5) Discuss the continuity of the function below at x = -3. Justify you work with limits. (x'+2x-5…

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!