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Use the graphs of $ f $ and $ g $ and their tangent lines at $ (2, 0) $ to find $ \displaystyle \lim_{x\to 2} \frac{f(x)}{g(x)} $.

$\lim _{x \rightarrow 2} \frac{f^{\prime}(x)}{g^{\prime}(x)}$

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Marina P.

March 22, 2021

Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. lim x?0+ (tan(5x))x

Oregon State University

Harvey Mudd College

University of Nottingham

So our goal is to find the limit as X approaches to of F. Of X over G. Of X. So um knowing what F. And G look like, it's best to look at their tangent lines at 20 So if we have photographs F. Of X. And then we divide that by G. Of X. What we see as a result is that we would get an indeterminant form as X approaches to. Yeah. Uh So as a result of that, what we do is we take the derivative of the numerator and the derivative of the denominator. That's what's known as the low Patel's room. So based on this, we would take their derivative at the numerator and denominator and take their limits as a result of this separately. And we would end up being able to get our answer. In this case we're looking specifically at 20. So we would evaluate the limit as X approaches to. This would give us a final answer. And this is the process by which we can carry out low petals rule when we have an indeterminate form and only when we have the indeterminate form

California Baptist University