Examine whether or not the function (4-x² f (x) =- [4+x if x<0 if x>0 Is continuous at x = 0

Q: Determine the domain of the function and prove that it is continuous on its domain using Theorems…

A: Given: f(x) = ln (9 - x 2) To determine: The domain of the function and prove that it is continuous…

Q: Find the domain of f(x) = 1/x and discuss the behavior of f near any excluded x-values.

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Q: Explain why the function g(x) = ln(4-x2) + square root of x+1 is continuous at every number in its…

A: Consider the given function g(x). The function g(x) is the sum of two functions f(x) and h(x).First…

Q: Find the value of the constant k so that f(x) is continuous for all real values of x where f(x) is…

A: Solution

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

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Q: Is there a real function f(x) that is differentiable only at a point x?

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Q: Sketch the graph of the function f(x). f(x) is continuous from the right at x = 3, but not from the…

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Q: Suppose that a function ƒ satisfies the following conditions for all real values of x and y: i) ƒ(x…

A: The given conditions are,

Q: Find the domain of f(x) = 3x/(x − 1) and discuss the behavior of f near any excluded x-values.

A: Given function is f(x)=3xx-1 Since domain is the set of all those input values for which the…

Q: The function f (x) = 3x² –4x-3 is continuous everywhere.

A: Given,             f(x)=3x2-4x-3

Q: Suppose that f(x) = 2 for x &lt; 3 and f(x) = -4 for x &gt; 3. (a) What is f (3) if f is…

A: For x&lt;3,f(x) = 2For x&gt;3,f(x) =-4Part (a) - f(3) = ? when f(x) is left continuous.f(3) =…

Q: Show that f is not differentiable at x = 1 and has a corner in its graph there. x 1

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Q: Use the definitions of increasing and decreasing functions to prove that       f(x) = x3 is…

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Q: Determine the domain of the function and prove that it is continuous on its domain f(x) = x2 / (x +…

A: fx=x2x+x14 The domain is the set of all values of x for which denominator is non-zero. That is,…

Q: Determine the domain of the function and prove that it is continuous on its domain f(x) = e - x 2

A: Consider the given function. fx=e-x2 The function is define for every real value of x. Hence,…

Q: Let ƒ be the function given by ƒ(x) = (x-2)²(x+3). For what values of x is f not continuous?

A: The given function is fx=(x-2)2·(x+3)(x-2)·(x+1) We have to find the values of x, for which f is not…

Q: Determine whether the function of f(x) is continuous at x = -1 x2 -1 f(x) ={ x +1 X + -1 -2 X = -1

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Q: Is the function continuous  f(x) = e^x / 1 - e^x

A: We need to check the continuity of the function

Q: 3. f(x) = v2x – 5 at x = 3 -

A: (3) Given function is fx=2x−5 We have check whether the function fx is continuous or not at x=3 For…

Q: Determine if the piecewise function is continuous at a. x-3 x + 3 f(x) = 1, x-3 a = 3 x = 3 O Yes,…

A: Topic- limit

Q: Consider a function f(x) = |x – 3|. a. Show that f (x) is not differentiable at 3. -

A: Given         f(x) =|x-3|

Q: Determine the domain of the function and prove that it is continuous on its domain f(x) = √(x2+9)

A: Solution:Given     f(x)=x2+9To find the domain of the function  and to prove f is continous on its…

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

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Q: Let a be a real valued constant. Find f' (x) = limħ→0 f(x+h)-f(æ) for f (x) = Vax h

A: Given, α be a real valued constant.  fx =αx  We have to find f'x = limh→0fx+h-fxh

Q: 3x if x 2

A: Given that a function of f(x) and we find value of k. We know that if a function is continuous at x=…

Q: Find the constant c that makes g continuous on (-0;0) x-2x-8 g(x) = a+1 if x+2 if X=-2

A: Continuity of a function at a point x=c : If function is defined at x=c and limx→c fx=fc then we can…

Q: Determine if the given function is continuous at a given value of x. 2. f(x) = x² - 4x – 2 at x = 1…

A: Since you have posted multiple questions i can do first three subparts as per our company guidelines…

Q: 8. Determine the natural domain of the function Vx–1 f (x)= x²-3x+2 in interval notation.

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Q: x +1 x 2

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Q: What is f (3) When x²-9 X-3 f(x) = x when XX3? Assume that f(x) is a function that is continuous for…

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Q: B. Determine whether f(x) (x - 3) (2x + 1) (x + 4) is continuous at x= 3.

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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: 4x-8 i- -2 x +3a

A:

Q: Determine whether the function f(x) = (2x + 1)/(2x2 - x - 1) is continuous: a) at 2; b) at 1.

A: It is given that, fx=2x+12x2-x-1We have to find that the function is continuous at   a 2 and b 1

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: Find x for which f(x) is not continuous: 3 x-1 f(x) =-+ x'x2 -1

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Q: Find the value of the constant ( a, b, or c) that makes the function continuous.

A: Given: fx=1x,x&lt;-1, x&gt;12ax+b,-1≤x≤12 if given function is continuous then limx→-1-fx=limx→-1+fx…

Q: Determine if the function is continuous or discontinuous at x=2. h(x) = x - 1, if x 22 2x- 1, if x<2…

A: if Left hand limit and right hand limit are equal then function is…

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

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Q: What is f'(x) at x = -1 of the function f(x)=x^-2 + (x^2)^(1/2) *

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Q: Discuss the continuity of the function. x2 – 4 f(x) X + 2 f is discontinuous at x =

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Q: Explain why f(x)=3x^2+1 is continuous at x=-2

A: Consider the function  f(x)=3x2+1

Q: If a function f is continuous at 0, show that g(x) = xf(x) is differentiable at 0 and find the value…

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Q: Determine if the function is continuous at the given point. 1 f(x) = {* - (x2 – 2 x 0 at x = 0.

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

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Q: x 2

A: Consider the function f(x)=x-1              ,       x≤02x2-3x+1    ,       0&lt;x≤23x3-x2          ,…

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: (c) Determine whether f (x) is continuous at x-2, where [4x+3, xs2 f(x)= 8-x, x2

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Q: If functions ƒ(x) and g(x) are continuous for 0&lt;=x &lt;=1, could ƒ(x)/g(x) possibly be…

A: According to continuity theorem if f(x) and g(x) are continuous on [0,1] then if g(x) ≠ 0 on [0, 1]…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.