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Question

Evaluate limx5π4[sinx+cosx], where [.] denotes the greatest integer function.

A
2
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B
1
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C
0
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D
1
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Solution

The correct option is A 2
sinx+cosx=2(12sinx+12cosx)

=2(cosπ4sinx+sinπ4cosx)

=2sin(x+π4)

limx5π4(sinx+cosx)
=2limx5π4(sin(x+π4))

=2(sin(5π4+π4))
=2(sin(6π4))

=2(sin(3π2))
=2(sin(π+π2))

=2(sinπ2)

=2
limx5π4[sinx+cosx]

=[2]

=[1.414]=2

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