Question
If f(x)={sinx,x≠nπ,nϵI2,otherwise and g(x)=⎧⎪⎨⎪⎩x2+1,x≠0,24,x=05,x=2, then limx→0g{f(x)}
Answer: Option D
:
D
limx→0g{f(x)}=limx→0⎧⎪⎨⎪⎩(f(x))2+1,f(x)≠0,24,f(x)=05,f(x)=2=limx→0⎧⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪⎨⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪⎩sin2x+1,sinx≠0,2andx≠nπ4,sinx=0andx≠nπ5,sinx=2andx≠nπ5,2≠0,2andx≠nπ4,2=0andx=nπ5,2=2andx=nπ=limx→0{1+sin2x,x≠nπ5,x=nπ=1+sin20=1+0=1
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:
D
limx→0g{f(x)}=limx→0⎧⎪⎨⎪⎩(f(x))2+1,f(x)≠0,24,f(x)=05,f(x)=2=limx→0⎧⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪⎨⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪⎩sin2x+1,sinx≠0,2andx≠nπ4,sinx=0andx≠nπ5,sinx=2andx≠nπ5,2≠0,2andx≠nπ4,2=0andx=nπ5,2=2andx=nπ=limx→0{1+sin2x,x≠nπ5,x=nπ=1+sin20=1+0=1
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