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Find the limit: as x approaches 0 lim((5/x)-(5/sin(x))

1 answer

5/x - 5/sinx
= 5 * (sinx-x) / xsinx

now use l'Hospital's Rule

5(cosx-1)/(sinx + xcosx)

and again

-5sinx/(cosx+cosx-xsinx)
= 0/2
= 0
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