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askme12345
How to find the equation and limits?
of 5/x-2 and y=x+4/x^2+9
question states: find the horizontal or oblique asymptotes and write their equation and also state in limit form
To find the horizontal asymptote you have to take the limit of the function at +- \[\infty\]
Because the idea is that as the function approaches +- infinity it approaches a certain y value.
can you explain how to so that with 5/x-2
I'm not sure what you're asking. Is 5 / (x-2) = f(x)?
If that was the case, you would write the problem like this: lim 5/(x-2) = x(5/x / 1 -2/x/1) = 0 x->\[\infty\]
Because as x approaches infinity, the denominator gets bigger and bigger causing the y value to get smaller and smaller (when you divide a number by a larger number it makes it smaller). Therefore, it would be the same for negative infinity. So you have a horizontal asymptote at y = 0
how do you figure out the equation if u dont mind answring