Which if the following statements are wrongS-I:Ltx→0e1x-e-1xe1x+e-1x does not exist e1x-e-1xe1x+e-1xS-II: If a∈R and f(x)=xae1x-e-1xe1x+e-1x, x≠00,x=0is continuous And differentiable ∀x∈R then a>1
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a
only I
b
Only II
c
Both I, II
d
Neither I nor II
answer is D.
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Detailed Solution
Ltx→0+ 1−e−2x1+e−2x=1−01+0=1 , Ltx→0− e−2x−1e−2x+1=0−10+1=−1∴ S - I does not existsf(x) is a continuous at x=0 ∴ f(0)=lim x→0f(x)=lim x→0xae1x-e-1xe1x+e-1x⇒a>0 At x=0 f(x) is differentiable ⇒limx→0f(x)-f(0)x-0 exists ⇒Lx→0xa-1e1x-e-1xe1x+e-1x exists ⇒a-1>0⇒a>1