Question

find the intervals on which the function is continuous.

y= x+1 / (x^2 -15x +56)

Answer 1

function is continuous at all points except where it is not defined.
So, it is indirectly asking you to find the domain of the function.

hint: any function gets undefined when the denominator gets zero.

Answer 2

Thanks!

Answer 3

yw

Answer 4

also, this is true only because the function is not a piecewise function.

Answer 5

Yeah, I don't understand those.
Like this one

Find the limit of f(x) as x approaches 3 from the right

f(x) { -2 if x < 3

Answer 6

x+2 if 3 <= x <= 5
7 if x > 5

Answer 7

from right means, coming towards "3", alittle more than 3, very close but not "3"
so we use the second function to evaluate that

Answer 8

How do I evaluate this ?
x+2 if 3 <= x <= 5

The answer is 5 but I don't know how they got it.

Answer 9

so, to begin with ou understood why we used the second definition?

Answer 10

Because x approaches 3 from the right

Answer 11

yes and so, x is greater than 3

now, it becomes a regular limit problem.
you solve it by direct substitution

Answer 12

\[
\lim_{x\to3^+}x+2=(3)+2=5
\]

Answer 13

Ah, I see. I get it now! Thank you so much!

Answer 14

yw