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Limit of tan [x]/x when x>0. [K] represents the largest integer less than or equal to k

Limit of tan [x]/x when x>0. [K] represents the largest integer less than or equal to k

Grade:12

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
4 years ago
ok we have to solve this by first principles
when
x → 0+
=> [x] = 0 (exact)
and hence
[x]/x = 0 (exact) => lim x->0+ (tan[x]/x) = 0
now
when
x → 0-
=> [x] = -1 (exact)
hence
[x]/x → – infinity
=> lim x-> 0- (tan[x]/x) = undefined

thus limit does not exist

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