Let the function be, f( x )= cosx ( #x03C0; #x2212;x ) We have to find the value of the function at limit ...

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Algebra of Limits

cosx 16 . lim

Question

cosx16. lim

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Solution

Let the function be,

f( x )= cosx ( π−x )

We have to find the value of the function at limit x→0 .

So we need to check the function by substituting the value at a particular point, so that it should not be of the form 0 0 .

If the condition is true, then we need to simplify the term to remove 0 0 form.

f( x )= cos0 ( π−0 ) = 1 π

Now, we found that it is not in 0 0 form.

From the definition of limits, lim x→a f( x )= lim x→a p( x ) q( x ) = p( a ) q( a ) .

So, we can directly calculate the value of limit from the above expression as:

lim x→0 cosx ( π−x ) = cos0 ( π−0 ) = 1 π

Thus, the value of the given expression lim x→0 cosx ( π−x ) = 1 π .

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