Evaluate the following limit
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Answered by
14
Answer:
lim_(xto0)((3^(2x)-1)/(2^(3x)-1))=lim_(xto0)({((3^(2x)-1)/(2x)).2x})/({((2^(3x)-1)/(3x)).3x})
=2/3.(lim_(2xto0)((3^(2x)-1)/(2x)))/(lim_(3xto0)((2^(3x)-1)/(3x)))
=2/3.(log3)/(log2)" "[becauselim_(yto0)((a^(y)-1)/(y))=loga]
=(2log3)/(3log2)=(log(3^(2)))/(log(2^(3)))=(log9)/(log8).
Answered by
13
Given expression is
If we substitute directly x = 0, we get
which is indeterminant form.
So, Consider again
can be rewritten as
can be further rewritten as
We know,
So, using this result, we get
Hence,
If we substitute directly x = 0, we get
which is indeterminant form.
So, Consider again
can be rewritten as
We know,
So, using this result, we get
Hence,
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