What is the type of the following function: f(x) = x² + 5 where the domain is Z and the codomain is Z O a. One to one (Injective) O b. Onto (Surjective) O c. One to one correspondence (Bijection) O d. None of the choices is correct O e. F is not a function

Q: Verify the conditions of Rolle's Theorem over the interval [3, 7] for the function f(x)= x²-10x+16…

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A: Given:  p(x)=x2+2x-15q(x)=x+1x-3r(x)=7-x

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Q: What is the type of the following function: f(x) = x+5 where the domain is Z and the codomain is R O…

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Q: Suppose the following function is defined as c*x^4 from 4 to 7 and O otherwise. What is c? Your…

A: The following function is c*x4 defined over 4 to 7 TO find c

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A: (a) In order to find the critical point equate the first derivative to 0.

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Q: 2. Evaluate the following functions using the given relations. f(1) = 4 ; f(2) =-1; f(3) =-3…

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Q: Consider the following piecewise function where c is a constant real number. Зx2 + 5с х 2 3x2 + 5c x…

A: For limit to be existing both left side limit and right side limit should be equal

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Q: Suppose that the functions fand g are defined as follows. 1 f(x) = 5x+4 g(x) =-3x+2 Find fg and f-g.…

A: The solution of the problem is given in the next step.

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Q: Which of the following functions has a removable discontinuity at a=1? x-1 (A @ =*_"- 8(x): x2 x2 B…

A: Topic :- Limits Only C is having removable disontinuity at a=1

Q: Determine whether  the following statement is true or false, and explain why. A critical number c is…

A: Solution:GivenA critical number c is a number in the domain of a function ƒ for which ƒ′(c) = 0 or…

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Q: Determine whether each of the following statements is true or false, and explain why. A critical…

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Q: f is also constant

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Q: Consider the following function. f(x) = x2 – 6x %3D (a) Find the critical numbers of f. (Enter your…

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Q: 3) Show that f = f, ху for the following function: ху (x° у) f(x. y) + In(x° + y30 ) 20

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Q: Consider the following. x + 7 f(x) =2- x - 56 Find the x-value (if any) at which f is not…

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Q: Consider the following. x + 7 f(x) = x2 - x - 56 Find the x-value (if any) at which f is not…

A: To find The values of x at which f is not continuous.

Q: ) = , 1 as x → 3+? What is true about this function f( x x2 -9 O f(x) O f(x) → 0 from below O f(x) →…

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Q: If the function f(x) is even, which of the following is ze an O bn ao nothing is zero

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Q: Each of the following formulas defines a function from Z to Z. Which functions are one-to-one but…

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Q: show me the is Continueus following function :- or not 1x/ at x =

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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:

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Q: 8. Decide if the following functions are onto. Prove your answers. (a) f(x) = x² – 1 (b) g(x) = 2x…

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Q: For each of the following two statements, give a counterexample to show that the state- ment is…

A: Counter examples for given statements to show false are:

Q: The functionf is defined as f(x) = (x – 5)(x + 6)². Answer the following - questions without using a…

A: Solution : fx=x-5x+62a. if fx=0x-5x+62=0x-5=0,x+62=0x-5=0,x+6=0x=5,x=-6roots are,x=5,-6

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A: Given function is: hx=14x-2if x≠-2-2if x=-2 To find: h-5, h-2 and h0. Solution: If x=-5 then…

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Q: For the piecewise defined function 0 < x <1 1<x < 2 x +1, 2<x (2 + x, f(x) = {x - 2, we have Select…

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Q: Let f be piecewise function defined as following: 72 – 18x + x2 • If r 49, the value of f(x) is…

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Q: Suppose that the functions u and w are defined as follows. u (x) =x²+4 w (6) - /x+5 Find the…

A: givenu(x)=x2+4w(x)=x+5therefore(u+w)(x)=x2+4+x+5(u-w)(x)=x2+4-x+5

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!