Q: Which c.d.f. F is of X is continuous at x=0?

Q: If f is differentiable at a , then f is continuous at a . True O False

A:

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

A: Rearrange the the given rational function. As the denominator tends to 0 the function is undefined.…

Q: a) Is f(x) continuous at x=2? Explain. b) What is the type of discontinuity of f(x)? c) On what open…

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Q: Answer true or false. If f is not piecewise continuous on [0, co>), then L{f(t)} will not exist.…

A: The given statement is

Q: If f is continuous at a number, x, then f is differentiable at x. True

A:

Q: For what value of b is             continuous at every x?

A: To find the value of a such that given function is continuous for every x. f(x)=a2x-2a,    x≥212,…

Q: Answer true or false. If f is not piecewise continuous on [0, co>), then {f(t)} will not exist. True…

A:

Q: Where is the function f(r,y) = x² + xy + y? %3D continuous? Enter 99 when done.

A: The solution are next step

Q: For what values of a is Jaʼx – 2a, x2 2 f(x) ( 12, x< 2 continuous at every x?

A: Given : The function is f(x) =a2x - 2a        , x ≥212,                     x&lt;2 .

Q: Answer true or false. If f is not plecewise continuous on [0, 00>), then {f(t)} will not exist. O…

A: Note that, L{f(t)}=F(s)=∫0∞e-stf(t) dt...(1)

Q: If f' is continuous on [a, b], show that 2 f(x)f'(x) dx = (F(b))? – (F(a)² %3D -

A:

Q: 9. If f is continuous and | f(x) da = 3, find æf(x?) dx.

A: We have to evaluate the given definite integral using the other definite integral.

Q: Consider the following. S-5x, F(x)={,2- 6X +9, x²-6x + 9, x > 6 Find the x-value at which f is not…

A: Consider the given piecewise function

Q: Which of the following functions are continuous on (-0, 0)? (a) ƒ(æ) = 1/x. (b) g(x) = Va. (c) h(x)…

A: Topic = Functions  Correct letter is C

Q: Determine whether the statement is true or false. f(t) : e-t- et 2 is continuous everywhere. O True…

A: Given that f(t)=2e-t-et Now, e-t-et =0 gives1et=etor, 1=e2tor, et=1or, t=0

Q: For what values of a is

A:

Q: Answer true or false. If f is not piecewise continuous on [0, ∞>), then L{f(t)} will not exist. True…

A: Given: Lets consider the given, that Lft will not exist if f is not piecewise continuous on [0,…

Q: For what values of b is - b b + 1' g(x) x? + b, x > 0 continuous at every x?

A:

Q: Prove or disprove: If f is continuous, then S s) dx = [r(1-x) dx.

A:

Q: Answer true or false. If f is not piecewise continuous on [0, ∞o>), then L{f(t)} will not exist. O…

A:

Q: Prove thait if y=f(x) f(x)=0 when x is a rotional number, then f(x)=0 for all x € R. is continuous…

A:

Q: Consider the function F(x) = | s(t) dt , where a is a constant and f is continuous everywhere. By…

A: Find we have to use definition of derivative.

Q: For what values of a is Ja'x – 2a, x 2 2 f(x) : \ 12, x < 2 continuous at every x?

A: Given function is Since f(x) is continuous for every x. So, f(x) is continuous at x=2.

Q: is Continuous and S' fldx=l6, find S xf(x*)a

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Q: Answer true or false. If f is not piecewise continuous on [0, co>), then £{f(t)} will not exist. O…

A:

Q: Let f(x) = } sin , for # 0. Is f continuous at 0? Justify. Can f be defined at 0 so that it's…

A: A function f(x) is continuous at a point x=a if  fa-0=fa+0=fa

Q: Assume f(x) is continuous on [a, b]. Prove that if f(x) > 0 for all x € [a, b], then S. f(x) dx > 0.…

A: Extreme Value theorem states that if a real-valued function f is continuous on the closed inteval…

Q: Let f be a continuous function such that | f(x) dæ = 5 and f(x) dx = 3. %3D | 4f(æ) dæ? What is the…

A: Recall: Properties of integral:  i)   ∫abf(x)dx=-∫baf(x)dxii) ∫abf(x)dx+∫bcf(x)dx=∫acf(x)dxiii)…

Q: Ler f : R → R be continuous. If f(c) > 0, prove there exists a neighborhood N of c such that f(N) >…

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Q: Suppose f: a,b] → R is continuous and faf=/ for all xie [a,bl Show that f(x)= 0 ft rEla,b).

A:

Q: What values must a and b take for f to be continuous everywhere?

A: Given that the function fx=ax1+4x2 ,      x&lt;0b    ,                     x=0tan-1xx ,…

Q: Use the definition to show that the function f(x) = → is continuous on the interval [c, o), %3D…

A: The given function is f(x)=1x2 .we have to show that f(x) is continuous on the intervel [c,∞)…

Q: Answer true or false. If f is not piecewise continuous on [0, ∞>), then {f(t)} will not exist. O…

A:

Q: iii If the discontinuity of ƒ is removable, redefine ƒ so that it's continuous at 0

A: This question related to the topic continuity of real analysis.

Q: Which of the following interval is f(x) = O (2, +∞0) O [2, +∞0) 0 (-∞0, +∞0) ○ (0, +∞) 1 Vx…

A:

Q: Which of the following functions is continuous at (0, 0 )? f( x, y ) = In ( x² + y² ) ху Оb.f (x, у…

A: Which function is continue at point x and y=0

Q: Explain why, if f is continuous over [a, b], there is at least one point cin [a, b] such tha 1 f(c)…

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Q: If X is continuous on the interval 0 to 10, t O True False

A: For a continuous distribution, and there exist infinite points.

Q: Suppose f(r) = (In z)e. What is f'(x)?

A: d/dx (f(x)g(x))= f(x)g'(x)+g(x)f'(x)

Q: If ƒ is continuous on [a, b] and, what can you conclude about ƒ?

A: the integral given to us is ∫ab|f(x)|dx=0

Q: Suppose f is continuous ont he closed interval [a, b). If F(x) is an antiderivative of f(x), for…

A:

Q: B/ For what value of a is fo continuous at every x? x? – 1, x< 3 { fx) = 2ах, x2 3

A: Our objective is to find the value of a for which f(x) is continuous at every x.

Q: If f is continuous on [a,b], then f(x)dx= π + A) True B) False f(x) dx

A: Given that f is continuous on a,b. ∫abπ fx dx = π ∫abfx dx Say that the statement is true or false.…

Q: Determine whether the statement is true or false. If f(x) is continuous at x = c, then so is f(x).…

A: Solution is given as below:

Q: 19. If f is continuous and o f(x) dr = 20, find | #f(x*) dx af(r²)dr

A: given ∫09f(x)dx=20  and we need to find ∫09xf(x2)dx=?

Q: If f(x) = is continuous at x=, Find A (Ar? Ax x2

A: Given: fx=x3,x&lt;12Ax2,x≥12 We know that any given functiony=fx is continuous at x=a If,…

Q: The pdf of a continuous RVX is given by f(x) = 5x*, where 0 <x< 1. o? = 05/252 02/150 025/36 049/111…

A: Given Data :  Random variable of probability density function is : fx=5x4       To Find : Variance :…

Q: Suppose f is continuous and F'(x) = f(x). J s(x)dx =3, f(x)dx = 4, [f(x)dx= 5, and F(1) =6, evaluate…

A: Here this is simple application of integration and differentiation please watch carefully.

Q: Is the following functions continuous or not at z = 0?

A: To check whether the following function is continuous at z=0fz=Rez1+z