Calc problem?
Find the limit of [1/(t x (1+t)^(1/2)) – (1/t)] as x approaches zero.
The answer is -1/2 according to my book, but I can’t get a rational answer. Please help.
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lim t–>0 [1/(t x (1+t)^0.5) – (1/t)]
= lim t –> [(1-(1+t)^0.5)/(t(1+t)^0.5)]
= lim t –>0 [(1+t)^0.5 – 1 – t)/(t + t^2)
Now, use L’Hopital’s rule to get:
= lim t –>0 [{1/(2(t+1)^0.5) – 1} / (1+2t)
Plug 0 in for t to get
= (1/2 – 1)/1
= -1/2
I hope this helps!
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