- #1
CanadianEh
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Hi there,
Quick question. For F(X)= X/Sin(X), is there a hole at X=0?
Thanks.
Quick question. For F(X)= X/Sin(X), is there a hole at X=0?
Thanks.
CanadianEh said:Hi there,
Quick question. For F(X)= X/Sin(X), is there a hole at X=0?
Thanks.
tiny-tim said:Hi CanadianEh!
At x = 0, obviously, it's 0/0, which is undefined (it's known as an "indeterminate form"), so yes in that sense there's a hole …
of course, F(x) does tend to a limit at as x -> 0
CanadianEh said:Thanks so much! Can you help me explain why there is an oblique asymptote?
CanadianEh said:When a linear asymptote is not parallel to the x- or y-axis, it is called either an oblique asymptote or equivalently a slant asymptote.
In the graph of X/Sin(X), there appears to be an asymptote at y=x
That's right.CanadianEh said:Ok, so NO oblique asymptote, correct?
tiny-tim said:uhh?
wot's an oblique asymptote?
Bohrok said:A slant asymptote
The general process for dividing functions involves first finding the common factors in both the numerator and denominator of the fraction. Then, the remaining terms in the numerator and denominator are divided separately. Finally, the resulting fractions are simplified and combined, if possible.
No, it is not possible to divide a function by zero. Division by zero is undefined and results in an infinite value, which is not a valid output for a function.
To handle a fraction with a variable in the denominator, you can use the concept of rationalizing the denominator. This involves multiplying the numerator and denominator by the conjugate of the denominator, which is the same expression but with the opposite sign in the middle. This will eliminate the variable in the denominator and allow for simplification.
Dividing by a function involves dividing each term in the numerator and denominator by the same function, while dividing by a constant involves dividing each term in the numerator and denominator by the same numerical value. Dividing by a function may result in a simplified expression, while dividing by a constant will not change the value of the fraction.
Yes, it is possible to divide two functions with different domains. However, the resulting quotient will have a restricted domain that is the intersection of the domains of the two original functions. This is because the domain of a fraction is limited by the domain of the denominator, which cannot be equal to zero.