Question

Determine whether f is continuous at x = c in the functions given below. Use the 3 conditions of continuity to justify your answer.

Answer 1

I am in need of help on letter C.

Answer 2

For letter A and B, I got the following answers.

Answer 3

A) The limit is undefined. The meaning of f is not defined at x = c and c is not in the domain of f.

B) The limit is continuous. The limit meets the requirements of all 3 conditions; f is defined at x = c, the left and right limits are the same, and the left and right limits equal each other.

Answer 4

a is not continuous at x=c.

b and c are continuous for all real numbers

Answer 5

I understand why B is continuos. But, why is C continuous?

Answer 6

because when x<2, the function is x-1. ( this is a piecewise function)
Now plug in any value that is lesss than 2 and see if you get division by zero or the sq rt of a negative number. No value of x will do this. so the first part of the piecewise function (x-1) is continuous.
the 2nd part of the function says that when x=2, then f(x) =2. so that's ok
the 3rd part says for all numbers greater than 2, then f(x)=2x. plug in anything greater than 2 and you will get a real number. That is you won't get division by zero or a sq rt of a negative number . So all three parts are continuous

Answer 7

ok?

Answer 8

Yes. Thank You =]