Post a New Question

Calculus- continuity

posted by .

Discuss the continuity of
f(x)= sin x/x^2 - 9
That is, state where is it continuous/discontinuous and why.


Here was my original answer.
sinx is cont. because it's a trig function. It's cont. at -2pi, pi, -pi, and 2pi.
x^2 is cont. because it's raised to a rational power.
-9 is cont. because it's a polynomial.

He then put x= -3 + 3? at the bottom of my work.

I'm guessing that's where it's discontinuous. So f(x) is discontinuous where x= -3 and 3

  • Calculus- continuity -

    f(x)= sin x/(x^2 - 9)
    Your answer is correct, but unfortunately incomplete.
    In the given case, the denominator (x²-9) equals zero at x=±3, precisely what your teacher referred to.
    When the denominator approaches zero, the function becomes infinite, and hence discontinuous.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

More Related Questions

Post a New Question