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a
log (1+x)0
b
x1+x0
c
ex>1+x for x>0
d
ex<1-x for x>0
answer is D.
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Detailed Solution
loge(1+x)-x=loge(1+x)-logeex=loge 1+xex= ln 1+x1+x+x22!+x33!+...<0, as 1+x<1+x+x22!+...+ ∴loge1+x0 x1+x-log 1+x=1-11+x-log 1+x =1-11+x+log 1+x<0, for n>0 ∴ x1+x0, for x>0 ∴ex>1+x, for x>0; ∴(c) is true ex-1-x=1+x+x22!+...-1+x =2x+x22!+x33!+...>0, for x>0 ∴ex>1-x, for x>0 Thus, ex<1-x, for x>0 is not true.