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Question

If 0<x<1 and y=12x2+23x3+34x4+, then the value of e1+y at x=12 is

A
2e
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B
12e2
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C
2e2
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D
12e
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Solution

The correct option is B 12e2
y=12x2+23x3+34x4+
=(112)x2+(113)x3+(114)x4+
=(x2+x3+x4+)+(x22x33x44)
=x21x+x+(x1x22x33x44)
y=x1x+ln(1x)
y+1=11x+ln(1x)
ey+1=e11x+ln(1x)=e11x×eln(1x)=(1x)e11x
at x=12, y=12e2

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