f(x)-2xa_1π , evaluate limi f (x)31. If the function fx) satisfies lim
Let the given equation be:
lim x → 1 f ( x ) − 2 x 2 − 1 = π
We have to find the value of lim x → 1 f ( x ) .
By further expanding the limits:
lim x → 1 ( f ( x ) − 2 ) lim x → 1 ( x 2 − 1 ) = π
On simplification, we get
lim x → 1 ( f ( x ) − 2 ) = π lim x → 1 ( x 2 − 1 ) lim x → 1 f ( x ) − lim x → 1 ( 2 ) = π ( 1 2 − 1 ) lim x → 1 f ( x ) − lim x → 1 2 = 0
On arranging the terms, we get
lim x → 1 f ( x ) = lim x → 1 2 lim x → 1 f ( x ) = 2
Thus, the value of lim x → 1 f ( x ) = 2 .
Let the given equation be:
We have to find the value of
By further expanding the limits:
On simplification, we get
On arranging the terms, we get
Thus, the value of
