Give algebraic or verbal justification for credit. 1. lim x --> 1 (x^2 - 1)/(x+1

Question

Give algebraic or verbal justification for credit.

1. lim x --> 1

(x^2 - 1)/(x+1) - (1)/(x)


2. lim x --> 8

sqrt(x+8) - 4/x-8


3. lim x--> 0

(1/x+5 - 1/x)/(x)


4. lim x --> 0

(arccos x)/sqrt(1-x^2)

Please help, more than one question asked. But these will give me all the scenarios I need study for my next exam! Full rating to anyone that can help!

Explanation / Answer

a).lim x --> 1 (x^2 - 1)/(x+1) - (1)/(x) =(x-1) - 1/x =-1 b).lim x --> 8 sqrt(x+8) - 4/x-8 =L hospital rule =(-0.5)/sqrt(x+8) - 4 =(-1/8) -4 =-33/8 =-4.125 c).lim x--> 0 (1/x+5 - 1/x)/(x) =(x-x-5)/(x^2)(x+5) =l hopital rule =0 d).lim x --> 0 (arccos x)/sqrt(1-x^2) =(pi/2)

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