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If the function f(x) satisfies lim(xrarr...

If the function f(x) satisfies `lim_(xrarr1) (f(x)-2)/(x^(2)-1)=pi`, evaluate `lim_(Xrarr1) f(x)`.

Text Solution

Verified by Experts

According to the problem,
`underset(xrarr1)"lim"(f(x)-2)/(x^(2)-1)=pi`
Now, `underset(Xrarr1)"lim"[f(x)-2]=underset(Xrarr1)"lim"[(f(x)-2)/(x^(2)-1).(x^(2)-1)]`
`=underset(xrarr1)"lim"(f(x)-2)/(x^(2)-1).underset(xrarr1)"lim"(x^(2)-1)`
`=pixx0=0`
`rArr underset(xrarr1)"lim"f(x)=2`
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