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Question

If limx4x(π4tan1x+1x+2)=y2+4y+5,

then y can be equal to?

A
1
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B
1
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C
4
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D
3
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Solution

The correct options are
B 1
D 3
limx4x(π4tan1x+1x+2)=y2+4y+5
=limx4x(tan11tan1x+1x+2)
=limx4x⎜ ⎜ ⎜1x+1x+21+1(x+1x+2)⎟ ⎟ ⎟=limx4x(12x+3)
=limx42+3x=42+0=2
y2+4y+5=2y2+4y+3=0
(y+3)(y+1)=0
y=1,3

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