11. Define f: R→ R by f(x) = 8x if x is rational and f(x) = 2x² + 8 if x is irrational. Prove from the definition of continuity that f is continuous at 2 and discontinuous at 1.

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

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Q: 4x +1 if x1 a.) Explain, using the defintion of continuity at a point why f(x) is NOT continuous at…

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Q: using Contiaiui the Continuity af the function: at the Conditions of 2 Yょ? 12

A: Introduction: To be continuous at a point, a function must be defined there. Its limit must exist…

Q: (x+1 Q. #7 For the function g(x) = 3 if x 2 constant "b" that makes g(x) continuous at x=2 Final…

A: g(x) is continuous    here we find value of b by using condition of continuous function

Q: I'm having trouble understanding the continuity questions, please see the attached screen shot.

A: We find left and right hand limit at x=0.Left hand limit = 1

Q: How can we determine continuity at a point?

A: We have to discuss about continuity.

Q: Use the definition of continuity to show that f is continuous at 2: f(x) = 3x2 – 2x + 1.

A: Definition of function continuity is: A function fx is said to be continuous at point x0 if and only…

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

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Q: Discuss the continuity of the function f(x)= [x², x≤1 1+x, x>1 at x = 1.

A: given function To find: continuity of the function at x=1