Question

Identify and remove removable the discontinuities of 1) f(x)=sin(x+1)/tan (x+1)

Answer 1

@Canada907cat
Do you know where the discontinuity is, with the function as it is?
Recall that
1. a discontinuity can be caused by the denominator becoming zero
2. tan(x)=sin(x)/cos(x).

Answer 2

I really don't know, this subject is completely
new to me.

Answer 3

It has discontinuity in \[x=-1+\pi/2 +k\pi]
All of them removable with putting the value of cos(x+1) instead of the f(x) in discontinuous points.

Answer 4

so would that mean that the discontinuity is at x=-1?

Answer 5

..Wow

Answer 6

The discontinuity is not at x=-1, but It is at x=-1+\pi/2.
discontinuity is not having one of this: 1)left limit 2)right limit 3)f(that point)
In this case the f(x) does not exist because of denominator

Answer 7

Okay well I have to choose either x=-1 or x=0 for the discontinuity
.

Answer 8

Its x=-1 because it makes the denominator zero.

Answer 9

Okay so the next part of the question is that can it be removed by making f(-1)=1 or can not be removed and based on what you just said I'm guessing it cannot be removed.

Answer 10

Yes it can be removed by setting f(-1)=1 because cos(x+1) is a continuous function which can be replaced in non discontinuous points of given f(x)
cos(x+1)=cos(-1+1)=1
Therefore we have both left n right limit and function value at -1. The modified function is continuous in point x=-1

Answer 11

oh okay that makes sense.

Answer 12

Also you have to remember that condition for being continuous is that left and right limit are both equal to the f(x) in the point you are analyzing continuity.

Answer 13

okay great thank you so can you help me one more question that has the same concept as the first one?

Answer 14

Make a new question!

Answer 15

okay will do.