3 b) Find values of x, if any, at which f is not continuous:f(x) =+2

Q: Suppose that f( is a continuous function. If f(#) da=4, then what is the value of T - f(x)] dæ ?…

A: To evaluate the given definite integral.

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: Consider g(x) = x!/5. Is g(x) differentiable at x=0? Is g(x) continuous at x=0?

A: Given function

Q: If f(x) is continuous on the interval [a, b] and a <c < b, | f(x) dæ is equal to then

A:

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: For what value of b, f(x) is continuous at every x? (a²x-2a f(x) = (12 x2 2 x< 2

A: As f(x) has two parts and both parts are continuous in given x so make continuous only at point x= 2

Q: Where is f(x) = x-5 x² –6x+5 discontinuous? f (x)is continuous everywhere o 5 o 1 о 5, 1

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Q: Suppose f' (x) = g (x) (x + 1) (x – 2)´, where g (s) is a continuous function which is always…

A: When f'(x)&gt;0 then function increasing when f'(x)&lt;0 then function decreasing

Q: x< x3 B- If f(x) = Ax? is continuous at x = ; Find A? HIN IN

A: We are given : f(x)=x3       , x&lt;12Ax2     ,x≥12 is continuous at x=12 Condition for f(x) to be…

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: 18. Suppose that f is a differentiable function such that f(g(x)) = x, and f'(x) = 1 1+(f(x))². Show…

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Q: Suppose that f is a function on the interval [1, 3] such that –1 < f(x) < 1 for all x and f(x) dx…

A: It is given that ∫13fxdx=0 and -1≤fx≤1.

Q: if x3 is continuous at x = 3

A: Given query is to find the value of c so that function is continuous at x = 3.

Q: For all but two choices of a, the function (x) = x if xS a and x' ifx > a will be discontinuous at…

A:

Q: Consider the function f(x) : Find the value of B such that (3x + B if x> 3* f(x) is continuous at x…

A: Given: fx=2x2+3  if x≤33x+B   if x&gt;3

Q: (b) Suppose that f(x) = SBx? – 3 if if xS2 (Bx+ 2 %3D Find the value of ß so that f(x) is continuous…

A:

Q: Suppose that f(1) = 1, f(4) = 6, f (1) = 7, f '(4) = 5, and f " is continuous. Find the value of xf…

A:

Q: If f is continuous on [a, b], then the horizontal line y = k for every k between f (a) and f (b)…

A: If function 'f'  is continuous on closed interval [a, b], and if f(a)≠ f(b), then for any number k…

Q: Find c such that the function Sx2 – 4 - 4 x c is continuous everywhere. c =

A: Here, the given function is: f(x)=x2-4, if x≤c10x-29, if x&gt;c To find the value of c such that the…

Q: Find a value of x, if any, at which/(x)= Vx- 27 is not continuous.

A: We will check the continuity of the function

Q: If a function f(x) is not defined at x-c, then it is not continuous at a close interval [a, c). * O…

A: We know that function is continuous at c if the 1) f(c) is defined 2)limit of f(x) exist, Here…

Q: (3) If the functions f(x) and g(x) are continuous 0sxS1, then f(x)/ g(x) is continuous on the…

A:

Q: 35. Given that f(z) is a continuous even function, then A 0 B D

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Q: B) If f is differentiable at x, then prove that f is continuous at x Is the converse true? Why

A:

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

A: From the given problem: 57).   fx=12x+1,x≤23-x,x&gt;2   As we know that, if L.H.L is not equal to…

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

A: Given- fx=xx2-4 To find- The values of x at which the function is not continuous. Concept used-  The…

Q: ind the values of c that make f continuous everywhere: { Sa² – c² if x 3

A:

Q: 16.C. If f is defined and continuous on R? to R and if f(xo) > 0, then is f positive on some…

A: Consider the provided question,   We need to show that, f is strictly positive on some neighborhood…

Q: If f(2) is a continuous function at a point z, , then f(z) is differentiable at z, . But the…

A: Authoring guidelines:…

Q: Suppose that f(x) = SBx? – 3 if if (Bx+2 x> 2 Find the value of B so that f(x) is continuous…

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Q: Use limits to determine if f(x) = is continuous at x = 1. z-2

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Q: 10 If f is a continuous function and F(x)=f(x) for all x€R, then | f(Gx)dx=?

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Q: Find c such that the function x ≤ c { is continuous everywhere. f(x) = x² - 3 X 6x 12 x > c -

A:

Q: 3. For what value of b, f(x) is continuous at every x? f(x) = {, x -2

A: Given that, fx=x         x&lt;-2bx2      x≥-2

Q: 1. If f:(0, 3) → R is continuous, must its range be an open (possibly infinite) interval?

A: Given statement is : If f:(0, 3) → R is continuous, must its range be an open (possibly infinite)…

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: Suppose that f(x) is continuous and differentiable, f(2) = -2, f(6) = -6, and f(x)dx =-10. Compute ,…

A: Topic:- Functions

Q: (e) If f(x) is continuous at x = 0, then what is the value of n: if 20 if x=0 f(x)=\ 38

A:

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

A:

Q: 2 2 If f is continuous on [0, 2] and / f(x) dx = 5, find the value of | f(x – 2) dæ.

A:

Q: Find a constant b such that h is continuous at x = 2, where x +1 for |x| 2 With this choice of b,…

A: It is given that the continuous function  hx=x+1for x&lt;2b-x2for x≥2 It is also given that function…

Q: Find the value of c so that f(x) is continuous at x = 3? x2 f(x) = x 3

A: Given query is to find the value of c.

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

A:

Q: Prove: f(x)=5x y is continuous at x=2

A: A function fx is continuous at a point x=a, if limx→afx=fa Given function is

Q: Use the e-d definition to prove that f(x) = x³ + 3 is continuous at xo = 3.

A:

Q: Find c such that the function x c is continuous everywhere. x² – 8 f(x) = {

A: ANSWER : c = 5

Q: (b) FIND the value of c, so that f(x) = {cx – 1, x< 0 lx² – 1. x 2 0 is continuous everywhere.

A:

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.