How do you find #lim cos(3theta)/(pi/2-theta)# as #theta->pi/2# using l'Hospital's Rule?

Answer 1

Look below

You need to see if the limit is in indeterminate form, so calculate the limit as #theta -> pi/2#
#cos(3(pi/2))/{pi/2-pi/2} = 0/0# which is indeterminate form

now do the derivative of the function

#lim_{theta->pi/2} d/dx[cos(3theta)/{pi/2-theta}]#
#d/dx [cos(3theta)] = 0#
#d/dx [pi/2-theta] = 0#
#0/0# is indeterminate form

so the limit doesn't exist

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Answer 2

To find the limit ( \lim_{\theta \to \frac{\pi}{2}} \frac{\cos(3\theta)}{\frac{\pi}{2} - \theta} ) using L'Hôpital's Rule, differentiate the numerator and the denominator separately with respect to ( \theta ) and then take the limit again. Repeat this process until you obtain a determinate form.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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