Question

(ii) Lim 1/xcos^-1 1-x^2/1+x^2
x → 0

​

Answer 1

Answer:

We know that

cos

−1

(

1+x

2

1−x

2

)={

2tan

−1

x,

−2tan

−1

x,

x≥0

x<0

RHL=

x→0

+

lim

x

1

cos

−1

(

1+x

2

1−x

2

)=

x→0

+

lim

x

2tan

−1

x

=2

LHL=

x→0

−

lim

x

1

cos

−1

(

1+x

2

1−x

2

)=

x→0

−

lim

x

−2tan

−1

x

=−2

Hence, LHL



=RHL

So, the limit does not exist.