The function has a vertical asymptote at x = 0.Ī word of caution: Do not evaluate the limits individually and subtract because ±∞ are not real numbers. Rewriting 1/ x 2 − 1/ x 3 as an equivalent fractional expression ( x − 1)/ x 3, the numerator approaches −1, and the denominator approaches 0 through positive values as x approaches 0 from the right hence, the function decreases without bound and. The function has a vertical asymptote at x = 2. The function has a vertical asymptote at x = 0 (see Figure ).Īs x approaches 2 from the left, the numerator approaches 5, and the denominator approaches 0 through negative values hence, the function decreases without bound and. The sign of the infinite limit is determined by the sign of the quotient of the numerator and the denominator at values close to the number that the independent variable is approaching.Īs x approaches 0, the numerator is always positive and the denominator approaches 0 and is always positive hence, the function increases without bound and. In general, a fractional function will have an infinite limit if the limit of the denominator is zero and the limit of the numerator is not zero.
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