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Q.

Let I1=limx  x  2xx3+x2+x3x3x2+x3 and I2=limx0extan(2025)x  1xln(1+x), then the value I1I2 is equal to 

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a

2025

b

4050

c

225

d

450

answer is D.

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Detailed Solution

I1=x2((1+α)1/3+(1β)1/32),α=1x+1x2,β=1x1x2

I1=x2((αβ3+13)(131)α2+β22)=29, I2=2025 

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Let I1=limx→∞  x  2x−x3+x2+x3−x3−x2+x3 and I2=limx→0extan(2025)x −  1x ln(1+x), then the value I1I2 is equal to