Is the following function continuous? [x² + y² _if x² + y² < 1 if x² + y² > ! f (x, y) =

Q: is uniformly continuous by definition on the interval (-1,1) . 4 - * Show that f(x) =

A: A function fx defined on an open intervala,b is uniformly continuous on a,b iff  i fx is continuous…

Q: Is f(x)= Vx + 1 continuous at x == -1

A: Draw the graph and check continuty with help of limit of function.

Q: Suppose that f: [0,1]–R is a function satisfying the conclusions of the intermediate value theorem.…

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Q: Suppose that f(x) is a continuous function on [a , b] and F(x)= | f(t) dt a Part 1 of the…

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Q: Examine if f(x) = x3sin(1/x) is uniform continuous on the interval (0,2]

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Q: Let f(x) = { *, if x= 2 ; for the eax if x + 2 function to be continuous at x = 2 the value of a is

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Q: Does there exist a continuous function f(x) such that f(0) all x in (0, 2)? 10, f(2) = 2 and f'(x)…

A: Let's find.

Q: 2. f(x) = Vx – 1 at x = 5

A: Function is continuous and differentiable both at x= 5.....for detail...go through the solution

Q: Prove that the function f(x) = 2x is uniformly continuous on R.

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Q: Is f(x) = -3 A. Yes B. Does Not Exist continuous at x = 3? C. No D. Cannot be determined

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Q: f(x)={x^2−9x≤c, 2x−10 x>c } i

A: Consider function f(x)=x2-9           x≤c2x-10        x&gt;c Now  limx→c+ f(x)=limx→c+…

Q: If functions ƒ(x) and g(x) are continuous for

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Q: Suppose that f (x) &lt; 0 if x is positive and f (x) &gt; 1 if x is negative. Can f be continuous at…

A: f(x) will be continuous at x = 0 if LHL = f(0) = RHL

Q: Show that f(x) = is uniformly continuous by definition on the interval (-1,1) . 4 - *

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Q: c. Show that f(x) is NOT uniformly continuous on [0, +∞).

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Q: Is there a continuous function such that - f: [1,2] U [3,4] → R - f(1) * f(4) < 0 - f(x) not egual 0…

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Q: 2. Show that the function, defined by f(x) = is NOT uniformly continuous on its x2 %3D domain D(f) =…

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Q: ずx 1

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Q: Let f(x) = CX– 2, x > I lx+ 8, x < 1 For what value of c is f(x) continuous on (-00, 0)

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Q: Consider a continuous function f(x)=2ex−1−2x. The graph of f is decreasing on which interval/s?

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Q: Can Rolle's Theorem be applied to f(x) = 1/(1-x) on interval [0,3]? If yes, what is c in (0,3) such…

A: here we can't apply the rolles Theorem

Q: Suppose that f(1)=8, f(4)=−4, f′(1)=−3, f′(4)=2, and f′′ is continuous. Find the value of ∫from 1 to…

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Q: The interval over which the function f(x) = becomes continuous is %3D x+8 (-3, 0) (-3, 3) (-00,…

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Q: Determine whether the function 2х + 1 f(x) %3D 2r2 2x2 – x – 1 is continuous: a. at 2; b. at 1.

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Q: What is the continuous extension of f(x) = x3-1 at point x-1. %3D x2-1'

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Q: Define f(2) in a way that extends f(s) = 2 to be continuous at s = 2. %3D -4

A: The function is defined as fs=s3-8s2-4.

Q: 4. Give an example of a continuous function f : (0, 1) → R that cannot be uniformly approximated by…

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Q: If a function f(x) is not defined at x-a, then it is not continuous at x-a.

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

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Q: show that f,given by f(x) x +0 )is continuous on R-{0}

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Q: Is the following piecewise defined function f(x) continuous at x = = 0, [cos(x), x≤0 f(x) = x²+x+1,…

A: The given function is: fx=cos x,       x≤0x2+x+1,  x&gt;0 Check whether the function is continuous…

Q: Determine the set of points at which the function is continuous. F(x, y) - х-у 1 + x² + y2

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Q: Determine the value of x of the continuous function: * х — 1 f(x) = {3x – 3 (-4x + 3 x 3

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Q: Use the definition to prove that the function in f(x) = 2x - 3 is uniformly continuous.

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Q: Suppose that f(1) = 5, ƒ(4) = -8, f'(1) = 4, f'(4) = -2, and f" is continuous. Find the value of |…

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Q: If f is continuous on [0, 1], prove that f₁¹ f(x) dx = f₁¹ ƒ(1 − x)dx.

A: This question can be solved using properties of definite integrals.

Q: Find the intervals on which the function is continuous. f (x) = { %3D 3, x = 2

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Q: Determine if g (x) = is continuous at x = 0

A: A function f(x) is continuous at x=a if, limx→af(x)=f(a). We try to evaluate limx→04-xx and f(0) and…

Q: If f is a continuous function and F'(x)=f(x) for all x € R, then - x)dx=?

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Q: Find m so that f(x) is continuous at x = 2. x +4 if x 2 -

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Q: Let f: (0,0) → (0, 0) be a function defined by f (x) =- for all x E (0, ∞). Prove that fis…

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Q: Let f be a function of multiplicity 5 at P. Then at P, u(x) = has multiplicity: f(x) f(x)'

A: Let, then has form of, Now, differentiating the above equation we get,

Q: Show that x³, if x 0 is not continuous at x = 0. %3D

A: According to the problem, we have

Q: h(x) = x+1 %3D at x = 1 x2-1

A: Function f(x) is continuous at a point x=a :Function should be defined at x=a, and  limx→a-f(x) =…

Q: Let f(x) = 2 cosh(4x) – e4x %3D Find the absolute maximum of f(x) on the interval [0, In 3].

A: The given function is                                         f(x)=2 cosh(4x)-e-4x We know that…

Q: Σ 1 is continuous function in R. Prove f(x) = 4 n=1 n' +x*

A: The given function is                                     f(x)=∑n=1∞1n4+x4 To show that the above…

Q: 5. Is the function given by g(x) = 4x³. 6x continuous on R?

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Q: Prove that there is no continuous function f : S² → S' such that f(-x) =-f(x) for all x € S².

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