# 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 power term in the product so that we can solve it more easily.

Taking log both sides-

log Z = { log am = m log a}

Now it gives us a form that can be reduced to log Z = Dividing numerator and denominator by to get the desired form and using algebra of limits we have-

log Z = if we assume then as xa y 0

log Z = Use the formula- log Z = log Z = Now it gives us a form that can be reduced to Try to use it. We are basically proceeding with a hit and trial attempt.

log Z = sin (A+B) = sin A cos B + cos A sin B

log Z = log Z= log Z = log Z = Use the formula- log Z = cot a – 0

log Z = cot a

Z = ecot a

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