The function f : R ∼ { 0 } → R given by f ( x ) = x 1 − e 2 x − 1 2 can be made continuous at x = 0 by defining f ( 0 ) as

Question

The function f : R ∼ { 0 } → R given by f ( x ) = x 1 ​ − e 2 x − 1 2 ​ can be made continuous at x = 0 by defining f ( 0 ) as

TestHub · Accepted Answer

lim x → 0 ​ x 1 ​ − e 2 x − 1 2 ​ lim x → 0 ​ x ( e 2 x − 1 ) e 2 x − 1 − 2 x ​ lim x → 0 ​ ( e 2 x − 1 ) + 2 x e 2 x 2 e 2 x − 2 ​ lim x → 0 ​ 4 e 2 x + 4 x e 2 x 4 e 2 x ​ = 1 .

Mathematics - Limits Question with Solution | TestHub

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