Find the Asymptotes f(x)=1/(x^2)

Problem

ƒ(x)=1/(x2)

Solution

1. Identify vertical asymptotes by finding the values of x where the denominator is zero and the numerator is non-zero.

x2=0

x=0

2. Verify the vertical asymptote by checking the limit as x approaches 0

(lim_x→0)(1/(x2))=∞

3. Identify horizontal asymptotes by finding the limit of the function as x approaches positive or negative infinity.

(lim_x→∞)(1/(x2))=0

(lim_x→−∞)(1/(x2))=0

4. Determine the horizontal asymptote from the results of the limits.

y=0

Final Answer

Vertical Asymptote: *x=0, Horizontal Asymptote: *y=0

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