Whether this function is continuous-- please help?

Question

Hi,

I would like to find out the answer to this question.

if

f(x) = 5*x-2 if x is less than 4

_____

√5(x-4) if x is greater than or equal to 4

the square root covers all of it

then out of the following which is correct... only one is correct.

1. though both left and right limits exist at x = 4, they are not equal.

2. the left limit does not exist at x = 4.

3. though the limit at x = 4 exists, the value of the limit is not equal to the value of the function at x = 4.

4. the right limit does not exist at x = 4.

5.None of the above

Thanks for any answers received.

It is much appreciated.

Answer 1

1.

Answer 2

4

Answer 3

for me it is true 2.nd answer... but I am not 100% sure...

good luck

Answer 4

Left limit at x=4

= 5*4 - 2 = 20 - 2 = 18

Right limit at x = 4

= √5(4-4) = 0

This shows that both limits exist but they are not equal.

Ans: (1)