Limits at infinity of quotients with trig (limit undefined) | AP Calculus AB | Khan Academy

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Sal analyzes the limit of (x_+1)/sin(x) at infinity. It turns out this limit doesn't exist, as the function keeps oscillating between positive and negative infinity.

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

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But the limit as x approaches infinity of sin(x) / (x^2 + 1) does exist because we're dividing by an extremely large number while sin(x) is bounded between -1 and 1 inclusively. It will oscillate between positive and negative but as a whole it approaches 0... 😊😊😊😇😇😇

reincarnate

My question is why does a limit exists when the denominator is cos x? Since both sin x and cos x are bounded between -1 and 1, both should be the same

CusPedro

can you please update our app it really crashes

namannarang

It's spelled existent not existant.

kumarsaurav

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This is a very famous limit

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