f(x) = jx+2 f [o,4) - IR Is it continuons? uniformlu contiauous HWI s? egui.continuous?

Q: 33. Let x² - 4y2 if x + 2y f(x, y) = 2y %3D | 8(x), if x = 2y %3D If fis continuous in the whole…

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Q: Evaluate the function shown, where ƒ is continuous on [3, 8], ƒ(3) = 4,and ƒ(8) = 20.

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Q: Find the interval that the fullowing function is continous at In (9 -x) %3D A. [I,3] BL) (3,3) (1,3)…

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Q: Explain why the Intermediate Value Theorem is not necess arily guaranteed fo f (x) = = CSC for x E…

A: Topic = Functions   The intermediate value theorem states that if f is a continuous function whose…

Q: Show that if u =x - y and v =r+ y, then for any continuous f, e-2s* f(x - y,x + y)dydr = || (a+n)e-…

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Q: For what values of b is b + 1' x? + b, x > 0 8(x) = continuous at every x?

A: Now we check the continuity at x = 0:

Q: Show that a function f : R? → R defined by S (7, y) = ! if (x, y) + (0,0) 0, if x = y = 0 is…

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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

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Q: Suppose f E R[0, 1] and let f() in An k=1 for all n. Prove that an → So f dx.

A: Given -  To Prove -

Q: Is the function continuous on the interval 0, 27? 1+(sin z)? O yes O no cannot be determined

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

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Q: Based on your work in part a, on what interval(s) is f(x) continuous?

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Q: Q2: If f(x) and g(x) are continuous on [a,b]and if f = [g Prove that 3c e[a,b] such that f(c) g(c).

A: From the given information. The functions f(x) and g(x) are continuous functions on [a,b]. The…

Q: Iff is continuous on [a,b], then rtf(x) dx = π f(x) dx 1 A True B) False

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Q: 6. Suppose that ƒ is differentiable on (a,b). interval [a, b]? Justify your response for find a…

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Q: . Apply Jensen's inequality (2) to f(x) = In x, with i 1 = ..= d = 1/n to prove that 1 Vx1x2...X 0,…

A: Given :-  Apply Jensen's inequality (2) to f  x  = ln x  , with λ1 = λ2 = ..........  = λn = 1n to…

Q: Iff is continuous at a point a and c e R, then cf is continuous at a.

A: Note that, f is said to be continuous at 'a' if limx→af(x)=f(a) And, (cf)(x)=cf(x)

Q: BLet f sohisfies the following data 3. 2. 2. Use Muller's mc th od to fnd a, st

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Q: Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (If…

A: Need to solve for C

Q: to verify thiIS 1 For which values of a ER is the function ax? f(x + iy) = (ax- ary) + i + ay 2 an…

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Q: For what value of a is

A: Given           f(x)=x2-1    ,  x<32ax       ,   x≥3

Q: For what value of b is Sx, g(x) bx?, x 2 -2 X<-2 continuous at every x?

A: The given function is gx=x,x&lt;-2bx2x≥-2. Assume that g is continuous function.

Q: 2. Do as indicated. if r m, r+1 a. Find all values of m such that g(r)= is continuous everywhere.…

A: Given function is: gx=x+1if x≤mx2if x&gt;m To find all values of m such that given function is…

Q: Show that the subtangent of f (x) = ex is everywhere equal to 1.

A: Formula to find the subtangent of the function helps to find the required subtangent. Derivative of…

Q: If f is continuous on [a, b], then ſ tf(x)dx =t f f(x)dæ Select one: O True O False

A: Given: f is continuous on a, b, then ∫t f(x)dx=t∫f(x)dx

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

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Q: The function f(x) interval [1, e] at x = Hora lo 0 x is the nat

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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: Let f(æ) = (4x + 26) In(æ + 3) %3D for æ > -3. Find the smallest value of A so that f(a) is concave…

A: Here we will find out the required condition.

Q: Consider the function f(x) = 8 – 8x2/3 on the interval [-1,1]. Which of the three hypotheses of…

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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: Which of the following tatements is true about a mooth function f at (a, b) it ² (a, b) c, fax (a,…

A: f has relative maxima at (a, b) if D&gt;0, fxx(a,b)&lt;0 f has relative minima at (a, b) if D&gt;0,…

Q: Find c such that the function 10 I C - is continuous everywhere.

A: A function f(x) is said to be continuous at a point x=a if limx→af(x)=f(a). That is, a function f(x)…

Q: (Read the dėlihition Caleluny.) |x2, if x l; is differentiable at 1. 2x-1, ifx > I; 4. Prove that…

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Q: On which of the following interval is f(x) S O (0, +∞0) ○ (2, +∞) O [2, +∞0) 0 (-∞, +∞0) 1 x-2…

A: We will the fact that root value should be positive.

Q: Find all volves of o,b ond c such that the func Ef×メ goo)= てメー1) 1チxg? 21 if x= 1 is continuous at…

A: Given, gx=ax3+bx2+cx+1x-12,  if x≠12,                               if x=1

Q: Find the value of a so that the function is continuous everywhere x2 + ax – 2, x 1 O 1 O 2 O 3 O 4 O…

A: Given:   f(x) = x2+ ax - 2  when x≤ 1     f(x) = x + 3 when x &gt; 1

Q: (5) Prove that if f is continuously differentiable on [a, b], then |f(a) – f(b)| a – b max f'(x)|…

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Q: - For what value of b is Sx, bx?, x2 -2 x<-2 х, g(x) = continuous at every x?

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Q: ) For a, 3 ER and B > 0, let f(x) ={} x° sin(|x|-#), when x # 0 when x = 0 0, ange of a and B (and…

A: Continuity and differentiability

Q: . For what value(s) of c is f(x) = 54-x³, x < 3) %3D lcx² + 13, x 2 3) continuous everywhere?

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Q: If x is a r.v. with c.d.f. F(x), F(x) is continuous at x = 10, then P(X= 10) = 0. True False

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Q: Find the value of "k", given that the following function f(z) is continuous at z = 3 (x² -6z + 8, >…

A: Continuity

Q: Where is f(a) not continuous? JAROMEN M 0 :-2 SE 4 O 0 02 O nowhere O-2 and 2 O-2 0 2

A: here in graph we see that function is not contineous at 2 and -2 value there is not contineous graph…

Q: (2) Is the function f(x) : R → R, sin a 1 ifa # πh,k & Z, ifa = Tk, k ε Z f (x) Borel measurable?

A: Consider the given function, fx=1sinxifx≠πk,k∈Z1ifx=πk,k∈Z   Thus, the given function have infinite…

Q: If f(x) is continuous with f(a)f(b) < 0, then the e Select one: O an indeterminable number of roots…

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Q: Answer all the following questions 1. Find the doma in of f(x) = x-4

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Q: If X is a continuous RV, prove that E(X) = [1- F(x)] dx – F(x) dx. %3D

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Q: If f:R → R is continuous at both 2 and 4, then f must be continuous at some c E (2,4). Select one:…

A: Consider the function f:R→R, that is continuous at both the points 2 and 4. Let there be a point c…