evaluate LIMITx_0[tan 5x+6x] /[tan3x+4x]
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lim x->0 (tan5x + 6x) /(tan3x + 4x)
use Leibniz rule,
=lim x->0 [ (logsec(5x)/5) + 6 ] /[ (logsec3x)/3 + 4 ]
put x limit
=[(logsec(0) )/5. + 6 ]/[ (logsec(0) )/3 +4 ]
=(1/5 + 6)/(1/3+4)
=(31/6)/(13/3)
=31*3/6*13
=31/26
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