Question

x‘“+x5+13, 11m 7m X71

Answer 1

Let the function be

f( x )= x 10 + x 5 +1 x−1

We have to find value of the function at Limit x→−1

So we need to check the function by substituting the value at particular point 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 )= − 1 10 + ( −1 ) 5 +1 ( −1−1 ) = ( 1−1+1 ) −2 = −1 2

Hence, from the definition of limits lim x→a f( x )= lim x→a p( x ) q( x ) = p( a ) q( a )

lim x→−1 x 10 + x 5 +1 x−1 = ( −1 ) 10 + ( −1 ) 5 +1 −1−1 = 1+( −1 )+1 −2 = −1 2

Thus the value of the given expression lim x→−1 x 10 + x 5 +1 x−1 = −1 2 .