Evaluate x−>0limx2tan(πsin2x)+(∣x∣−sin(x[x]))2 , where [⋅]=G.I.F (A) π+1 (B) π (C) −1 (D) Does not exist

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Question

Evaluate $x - > 0 lim \frac{tan ( π sin ^{2} x ) + ( ∣ x ∣ - sin ( x [ x ] ) ) ^{2}}{x ^{2}}$ , where $[\cdot] = G . I . F$ (A) $π + 1$ (B) $π$ (C) $- 1$ (D) Does not exist

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Evaluate

x - > 0 lim \frac{tan ( π sin ^{2} x ) + ( ∣ x ∣ - sin ( x [ x ] ) ) ^{2}}{x ^{2}}

, where

[\cdot] = G . I . F

(A)

π + 1

(B)

π

(C)

- 1

(D) Does not exist

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Question Text

Evaluate

x - > 0 lim \frac{tan ( π sin ^{2} x ) + ( ∣ x ∣ - sin ( x [ x ] ) ) ^{2}}{x ^{2}}

, where

[\cdot] = G . I . F

(A)

π + 1

(B)

π

(C)

- 1

(D) Does not exist