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How do you evaluate the limit #sin(3t)/(5t)# as t approaches #0#?

Answer 1

Samantha Adkison

#3/5#

we'll shoe horn this into well known limit #lim_{z to 0} (sin z)/z = 1#

#lim_{t to 0} (sin (3t))/(5t)#

#=lim_{t to 0} 3/5 (sin (3t))/(3t)#

let #z = 3t#

#=lim_{z to 0} 3/5 (sin (z))/(z)#

#= 3/5lim_{z to 0} (sin (z))/(z) = 3/5#

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Answer 2

Aurora Alvarado

The limit of sin(3t)/(5t) as t approaches 0 is equal to 3/5.

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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.

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