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Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. If l'Hospital's Rule doesn't apply, explain why.
$ \displaystyle \lim_{x\to 0} \sin 5x \csc 3x $
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01:07
Wen Zheng
00:45
Amrita Bhasin
Calculus 1 / AB
Calculus 2 / BC
Chapter 4
Applications of Differentiation
Section 4
Indeterminate Forms and l'Hospital's Rule
Derivatives
Differentiation
Volume
Campbell University
Harvey Mudd College
University of Michigan - Ann Arbor
Idaho State University
Lectures
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Find the limit. Use l'…
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those problems were going to be possibly using the look tells road to solve the problem, but it's not always necessary. So we see that the function were given that we want to find the limit of Is sign five x. At times if you can three X. Which is the same thing as over the sign of three acts, then we plug in zero. We see that we would get zero or zero. This is an indeterminant form. So we can take the derivative of the numerator that would end up giving us five co sign Perfect. And then in the denominator that would give us three co sign three acts as we see. We can actually use local trials role in this case because we get the indeterminate form. Uh and then when we plug in zero, this time we get five times coastline of zero, which is just five and three times co sign of zero, which is three. So five thirds will be the final answer.
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