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Question

The value of limh0 2⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪3sin(π6+h)cos(π6+h)3 h(3coshsinh)⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪ is :

A
34
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B
23
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C
43
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D
23
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Solution

The correct option is C 43
limh0 2⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪3sin(π6+h)cos(π6+h)3 h(3coshsinh)⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪
=limh0 423⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪cos(π6)sin(π6+h)cos(π6+h)sin(π6) h[cos(π6)coshsinhsin(π6)]⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪
=limh0 23⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪sin(π6+hπ6) h(cos(h+π6))⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪
=limh0 23⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪sin(h) hcos(h+π6)⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪
=23×23=43

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