Let f (x) = X 3 2 — 1 x 2 x = = 2 Which of the following statements. I, II, and III, are true? 1. lim f(x) exists x→2 II. f (2) exists III. f is continuous at X Main Content = 2 only I I and II non of them all

Q: (3-х, х <2 +1, x 2 2 B. Is the function h(x) continuous at x-2?

A:

Q: Define g(-5) in a way that extends g(x)= 9(-5) = x² - 25 x + 8x + 15 to be continuous at x = -5.

A: We have to define g(-5) such that g(x) is continuous at x = -5.

Q: (b). Show whether (*) is continuous at *=-2, if (3x-2 for x = -2 S(x)=. x? - 4 х- 2 for x * -2

A:

Q: All statements below are false. Provide a counterexample of f and g each. (a) If f + g and fg are…

A:

Q: Which series converge in the interval described by |x| < 1? 1. 1+x+x^2+... 2. x+x^3 + x^5+... a.…

A:

Q: mx 10 if x < - 4 Let f(x) = x² + 8x - 6 if x ≥ - 4 If f(x) is a function which is continuous…

A:

Q: 3. State where the function below is continuous using interval notation. if x<2 4 f(x) = 3 if x 2

A: To check whether the given function is continuous using interval notation.…

Q: Va – V22 lim x → 22 х — 22 - (Use

A:

Q: f(x) x² - 2x - 8 { *2-22-3 x-4 x = 4 x‡4

A:

Q: f(2) = 4 and f(3) = 3. With this information, can you determine whether there exists a real number c…

A:

Q: Find the value of the constant a that makes the following function continuous on (-∞, ∞). 5x³ + 5x²…

A: We need to find a value that makes the function continuous.

Q: ii) f(x) = x*-1 %3D x²-1

A:

Q: 1. From the graph, determine the function f (x) is continuous at x = -1. f(x) 3 %3D %3D -5 -4 -3 1…

A:

Q: 58. Show that if f is a function and z = x+h, then f(2) – f(x) _ f(x+ h) – f(x) Z - x h

A: This question is taken from the function in which we have to prove the given equation. We can write…

Q: Check the continuity of the function f(x) at x = -2 f(x) = - 6r + 3x l-6x if xs-2 if x>-2

A: Given,         The function fx at x=-2.           fx=x2+3xif x≤-2x3-6xif x&gt;-2

Q: x < 2 2 < x < 5 at x = 2 and 5. x 2 5 4х, 2. Classify the discontinuity of f (x) = } x + 6, x² – 1,…

A:

Q: 2. Identify the type of discontinuity of the function fx* – 2, l1– 2x, -2 2 f(x) = A. Infinite B.…

A: If the left-hand side of the limit is not equal to the right-hand side limit, then the function will…

Q: Q1) Check the continuity of the given function at the given c (or c's). 2-4z+3 if I+ 3 { (a) f(x) =…

A:

Q: Is the following function continuous? x2 – 9 if x 3 if x = 3

A: The function is given by