3. Determine the value of a so that f(x) is continuous on the entire real number line when: f(x) = (3x2, lах — 4, х < 1

Q: -1 if f(x) = xtan ,"x,find f' (/3 )by first principle

A:

Q: 8. Find all the points in the interval [1,5] for f(x) = -x² + 6x – 6 such that the function verifies…

A:

Q: 2. ASSUME f(x) IS CONTINUOUS AND DIFFERENTIABLE ON AN OPEN INTERVAL AS GRAPHED. WHICH OF THESE…

A: Since you have posted multiple question in this question so I have solved first question as per our…

Q: Find conditions on a and b that ensure f (x) = x3 + ax + b is increasing on (−∞,∞).

A: Consider the given function as fx=x3+ax+b

Q: Suppose that f(x) = βx2 − 3     if x ≤ 2                                βx + 2       if x &gt; 2…

A:

Q: 02: Let f(x)= x' – 7x+ 2, 0sxs1. 1. Show that f(x) has exactly one real root in the indicated…

A: Answer

Q: Where is f(x) = x-5 x² –6x+5 discontinuous? f (x)is continuous everywhere o 5 o 1 о 5, 1

A:

Q: 2. Given that f(x) = Vx+1 and g(x) =x² -9, find |(x) and give its domain in interval notation.

A:

Q: [3, 5]. - Calculate Rg for f(x) = 7 – x over R8

A:

Q: Which is the correct conclusion about the function h(x) ={V4- x2 if x - 3 if h has a removable…

A: Given function is: hx=-x-2    ;  if x&lt;-24-x2     ;  if -2≤x&lt;2x-3  ;  if x&gt;2 We have to…

Q: Consider the piecewise function: |x- 1| x² – 1' x <1 f(x) = (Ax² + 6, x 2 1 For what real number A…

A:

Q: Find the constant a such that the function is continuous on the entire real line. 7sin x if x <0…

A: For a function to be continuous at x = a, it must satisfy the following condition:

Q: Prove that f(x) = x 2 takes on the value 0.5 in the interval [0, 1].

A: We have to prove that f(x)=x2 takes on the value 0.5 in the interval [0, 1].

Q: Which of the following statements is not true, 3x² + 4x – 4 if x 1 f is discontinuous at æ = f is…

A: Given, f(x)=3x2+4x-44x2+7x-2,if x≤-1x2+3x+3,if-1&lt; x&lt;14x+5if x≥1 now put x=-2 in funcion…

Q: * 4. Determine a constant k for which the following function will be continuous on (-00,00). 3x + k,…

A: Solution of question as follow

Q: Consider the following. f(x)= x-5 / x2+3x-40 Find the x-values at which f is not continuous. Which…

A:

Q: (b) Redefine f(4) so that f is continuous at x = 4 (and thus the discontinuity is "removed"). f(4) =

A: The given function is: f(x)=x2-12x+32x-4

Q: Sßx² – 3 (Вх + 2 if (b) Suppose that f(x) if Find the value of ß so that f(x) is continuous…

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Q: Calculate the  M6  approximation for  f(x) = 4(x + 18)  on  [5, 8].   M6 =

A:

Q: Find the constant a such that the function is continuous on the entire real line. 8sin x if x < 0…

A: For continuity of f(x) LHL=RHL     so find lhl and rhl and equate both to get a.

Q: 4 If f(x) = x 2 - function for all real values of x, then f(8) is equal to

A:

Q: For what value of a is x² -1, x< 3 f(x) 2ax, x2 3 continuous at every x?

A: Given function is Since, f(x) is continuous at every x, so f(x) is continuous at x=3.

Q: Find the constant a such that the function is continuous on the entire real line. 8sin x If x < 0 if…

A:

Q: Q2) Discuss the continuity at x=2. When: x> 2 x = 2 3x + 1 f(x) : x² + 3 %3D 2x + 1 x< 2

A: The given functionf(x)=3x+1x&gt;2x2+3x=22x+1x&lt;2to check continuity at x=2

Q: Consider the following f(x)= 2/4-x2 Find the x-values at which f is not continuous. Which of the…

A:

Q: Suppose that the function f: [0, 1] in R is continuous and thatf(x) &gt; 2      if 0&lt;=X &lt; 1.Is…

A:

Q: Suppose that f(x) = βx2-3     if x≤2                                   βx+2       if x &gt; 2…

A:

Q: 1. f (x) = 3x² + 2x + 1 at x = -2

A: Given that:                            1. f(x)=3x2+2x+1                 at x=-2.2. h(x)=x+1x2-1 at…

Q: Prove that f (x) = x2 takes on the value 0.5 in the interval [0, 1].

A: Here given

Q: 29- For uhat values of a and b is ax+2b x+3a-b くXS2 3X-5 Continuous at every X

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

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: Suppose that f (0) = 2 and f' (x) ≤ 3 for x &gt; 0. Apply the MVT to the interval [0, 4] to prove…

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Q: Prove that the functionsf(x)=√x2+4x+3 and g(x)=x3+2x2 / x2+1are asymptotically equal to each other…

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Q: Calculate M6 for f(x) = 5 · In(æ³) over [1, 2].

A: Given:   f(x)=5.ln(x3) over [1,3]

Q: Find the value of c such that (-)- { S22 - c²;. x 4 is continuous on the real numbers.

A: Given Data: Function: gx=x2-c2; x&lt;4cx+20; x≥4 The limit of g(x) tending to the right of 4 is,…

Q: - 35) Prove that if y=flx)is continuoUS and flx1= 0 when x is a rational number, then f Lx)=0 for…

A: The objective is to show f(x) =0 for all x belongs to R.

Q: 3. Apply the three conditions of continuity to determine if the function f(x) = 2x²+5x+2 x²-x-12 is…

A:

Q: Consider the following. 6 = f(x) = -x² +9 Find the x-values at which f is not continuous. Which of…

A: Given: As nothing is mentioned, we will be answering by graphical method. Graph:

Q: (b) Suppose that f(x) = ൜βx2 − 3    if x ≤ 2βx + 2      if x &gt; 2 Find the value of β so that f(x)…

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

Q: Find the constant a such that the function is continuous on the entire real line. (9x², Flx) = {9x?,…

A: Given function is : fx=9x2    ,      x≥1ax-6   ,    x&lt;1 Here given that function is continuous…

Q: + The f(x) = Undefined at x = -3 %3D TO F O

A: Given: f(x)= x-13-x A function is undefined at a point x=a, if the denominator of f(x) is 0 at x=a

Q: Find the values of a and b such that the following function f(x) = 2a cos(x + 1) - b.5x+2, if x -1,

A:

Q: Find the constant a, such that the function is continuous on the entire real line. ( 2x², f(x) = if…

A: Given the function is f(x) = 2x2,if  x≥1ax-1,if  x&lt;1

Q: a) Suppose that f(x) = 4x if x<-1 = cx + d if – 1<x< 2 = -5x if x 2 2 Find values of c and d such…

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Q: 9. Discuss the continuity of the function x 2 x2,

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Q: (b) Suppose that f(x) =  βx2 − 3            if x ≤ 2 βx + 2             if x > 2 Find the value of β…

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Q: 29 - For uhat values of a and b is ax+2b x+3a- b くXS2 3X-5 Continuous at every X ?

A:

Q: Find e so that f(x) is continuous on the entire number line. if x3

A: fx=x2    if  x≤3cx    if  x&gt;3 Since the given function is a polynomial function for all x&lt;3…

Q: 5. Find the value of k that makes the following function continuous. f(x) : ={2x - 1,if x2-1

A:

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!