Q. 435.0( 1 Vote )

# 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 ∞-∞, .. etc.)

Let Z = =

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

TIP: Most of the problems of logarithmic and exponential limits are solved using the formula and

As Z =

Z = {using algebra of limits}

Z =

Z = { sin(x-π/2) = -cos x}

As xπ/2

x-π/20

Let x-π/2 = y and y0

Z can be rewritten as-

Z =

Dividing numerator and denominator by sin y to get the form present in the formula

Z =

Using algebra of limits:

Z =

Use the formula: and

Z =

Hence,

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