Evaluate the following limit. DO NOT USE L'Hospital Rule?

Answer 1

#lim_(xrarr0)sin(12x)/(3x) = 4#

Without using Rules De L'Hospital :)

#lim_(xrarr0)sin(12x)/(3x)#
#x=u/12#
#x->0# #u->0#
#=# #lim_(urarr0)sinu/(cancel(3)*u/cancel(12))# #=# #lim_(urarr0)sinu/(u/(4)# #=# #lim_(urarr0)(sinu/1)/(u/4)# #=# #=# #lim_(urarr0)4sinu/u# #=# #4lim_(urarr0)sinu/u# #=# #4*1# #=# #4#
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Answer 2

A different way to find the limit

We shall use the well-known result #lim_(theta->0) sin theta/theta=1# and the limit constant multiple rule #limaf(x)=alimf(x)#
Also, notice #sin(12x)/(3x)=(4sin(12x))/(4(3x))=4*sin(12x)/(12x)#
#therefore lim_(x->0)sin(12x)/(3x)=4lim_(x->0)sin(12x)/(12x)=4*1=4#
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Answer 3

To evaluate the limit without using L'Hospital's Rule, we can try to simplify the expression or apply other limit properties. However, since you haven't provided the specific limit expression, I am unable to provide a direct answer. Please provide the limit expression so that I can assist you further.

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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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