# Evaluate the following limits:

As we need to find

We can directly find the limiting value of a function by putting the value of the variable at which the limiting value is asked if it does not take any indeterminate form (0/0 or ∞/∞ or ∞-∞,1 .. etc.)

Let Z =

As it is taking indeterminate form-

we need to take steps to remove this form so that we can get a finite value.

Z =

Take the log to bring the term in the product so that we can solve it more easily.

Taking log both sides-

log Z =

log Z =

{ log am = m log a}

log Z =

{using algebra of limits}

Still, if we put x = ∞ we get an indeterminate form,

Take highest power of x common and try to bring x in denominator of a term so that if we put x = ∞ term reduces to 0.

log Z =

log Z =

log Z =

log Z =

{ log (3/4) is a negative value as 3/4<1}

Loge Z = -∞

Z = e-∞ = 0

Hence,

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