NTA Abhyas JEE Main2020MathematicsContinuity and DifferentiabilityPractice

If the function f x = 1 - x 2 tan ⁡ π x 2 is continuous at x = 1 , then f 1 is equal to

Options

A1 π
Bπ 2
C0
Dπ

Correct answer

A. 1 π

Step-by-step solution

f 1 = l i m x → 1 f x = l i m x → 1 1 - x 2 tan ⁡ π x 2 Put x = 1 + h = lim h → 0 ⁡ 1 - 1 + h 2 tan ⁡ π 2 1 + h = lim h → 0 ⁡ - h 2 tan ⁡ π 2 + π h 2 = lim h → 0 ⁡ - h 2 - cot ⁡ π h 2 = l i m h → 0 π 2 ⋅ h tan ⁡ π h 2 ⋅ 1 π = 1 π

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