Question

Determine for what numbers, if any, the given function is discontinuous.

f(x) =

A. 5

B. None

C. 0

D. -5, 5

Answer 1

discontinuous at 5 since the function changes at that point. graphically, the limit approaching 5 from the left is different than the one from the right

Answer 2

so the answer is 5

Answer 3

yes. not -5

Answer 4

ok cool thanks @Euler271

Answer 5

i have one more if you dont mind @Euler271

Answer 6

Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit properties can be applied.



A. 16

B. does not exist

C. -16

D. 0

Answer 7

you need to apply l'Hopitals rule which states that.

\[\lim_{x->a} \frac{ f(x) }{ g(x) } = \lim_{x->a} \frac{ f'(x) }{ g'(x) }\]

this is used when the limit the first time around gives 0/0 or inf/inf

Answer 8

ok

Answer 9

what do you do next

Answer 10

you would do plug in x = 1 again.

so taking f'(x)/g'(x) gives:

\[\lim_{x->1}\frac{ 3x^2 + 10x + 3 }{ 1 } = 16\]

Answer 11

thank so so so so much for all your help @Euler271 I truly appreciate it ;-)

Answer 12

:)