If f x = tan ⁡ x 2 , x ∈ 0 , π 3 , then f ′ π 4 (where, . is the greatest integer function)

Question

If f x = tan ⁡ x 2 , x ∈ 0 , π 3 , then f ′ π 4 (where, . is the greatest integer function), is equal to 1, is equal to 0, does not exist, None of these

MARKS App · Accepted Answer

LHD : f ' π 4 = lim h → 0 + f π 4 − h − f π 4 − h = lim h → 0 + ⁡ tan ⁡ π 4 - h 2 ⁡ - tan ⁡ π 4 2 - h = lim h → 0 + ⁡ 0 - 1 - h → ∞ ∴ f ' π 4 does not exist.

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