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Question

limh0a+h2 sin a+h-a2 sin ah

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Solution

limh0a+h2 sin a+h-a2 sin ah

= limh0a2 sin a+h + h2sin a+h+2ah sina+h - a2 sin ah= limh0a2sina+h-sinah+h2sina+hh+2ah sina+hhDividing and multiplying the denominator by 2: limh0a22cosa+h+a2 sina+h-a22×h2+hsina+h+2a sina+h= limh0a2cos a+h+a2+h sin a+h+2a sin a+h= a2 cos a+0+2a sina= a2 cosa + 2a sina

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