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Q.

The value of limx01xtan1x+12x+1π4 is

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Detailed Solution

 Limit π/4=tan11 Use 

tan1xtan1y=tan(xy)1+xy
limx01xtan1x+12x+1π4 =limx01xtan-1x+12x+1-1x+12x+1+1 =limx01xtan-1-x3x+2 =-limx0tan-1x3x+2x3x+23x+2=-12
 

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