If the function f ( x ) = t a n x − s i n x t a n ( t a n x ) − s i n ( s i n x ) is continuous at x = 0 , then f ( 0 ) is equal to ________

Question

If the function f ( x ) = t a n x − s i n x t a n ( t a n x ) − s i n ( s i n x ) ​ is continuous at x = 0 , then f ( 0 ) is equal to ________

TestHub · Accepted Answer

lim x → 0 ​ x 3 t a n x − s i n x ​ t a n 3 x t a n ( t a n x ) − t a n x ​ x 3 t a n 3 x ​ + x 3 t a n x − s i n x ​ + s i n 3 x s i n x − s i n ( s i n x ) ​ x 3 s i n 3 x ​ ​ = 2 1 ​ 3 1 ​ + 2 1 ​ + 6 1 ​ ​ = 2

Mathematics - Limits Question with Solution | TestHub

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