limit x----> infinity ((x-5)/(x-2))^(x-3) is ?

Since 

Now let's evaluate the limits of both the functions separately,

apply infinity property,

=1

Now,

Now apply the limit chain rule,

Now evaluate 

Now let's apply the L'Hospital's rule to evaluate the limit,

Test L'Hospital condition=0/0

Now again apply L'Hospital's rule,

Now again apply L'Hospital's rule,

=-3

Since 

Now let's evaluate the limits of both the functions separately,

apply infinity property,

=1

Now,

Now apply the limit chain rule,

Now evaluate 

Now let's apply the L'Hospital's rule to evaluate the limit,

Test L'Hospital condition=0/0

Now again apply L'Hospital's rule,

Now again apply L'Hospital's rule,

=-3

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