If the function f defined on - 1 3 , 1 / 3 by f x = 1 x l o g e 1 + 3 x 1 - 2 x , when x ≠ 0 k , when x = 0 , is continuous, then k is equal to.

Question

If the function f defined on - 1 3 , 1 / 3 by f x = 1 x l o g e 1 + 3 x 1 - 2 x , when x ≠ 0 k , when x = 0 , is continuous, then k is equal to.,

MARKS App · Accepted Answer

lim x → 0 ⁡ f x = lim x → 0 ⁡ ln ⁡ 1 + 3 x x - ln ⁡ 1 - 2 x x = lim x → 0 ⁡ 3 ln ⁡ 1 + 3 x 3 x + 2 ln 1 - 2 x - 2 x = 3 + 2 = 5 lim f x → 0 ln 1 + f x f x = 1 ∴ f x , will be continuous if f 0 = lim x → 0 ⁡ f x Thus, k = 5

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