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Evaluate the limit or state that it does not exist (you must have evidence and show work to get any credit).
A) lim x → 2
x^4 -x^2 -12/ x-2
= (x^2+3) (x^2-4)/ (x-2)
=(x^2+3) (x-2) (x+2)/ (x-2)
=(x^2+3)(x+2)
=(2^2 +3)(2+2)
=28
B)lim x → 1
√(x^2+1) –√(x+1)/(x^2+x-2)
=√(x^2+1) –√(x+1)/ (x^2+x-2) x √(x^2+1) +√(x+1)/√(x^2+1) +√(x+1)
=(x^2 +1-x+1) / (x^2+x-2) (√(x^2+1) +√(x+1)
=(x^2-x) / (x^2+x-2) (√(x^2+1) +√(x+1)
= x(x-1)/ (x-1) (x+2) (√(x^2+1) +√(x+1)
= x/ (x+2) (√(x^2+1) +√(x+1)
=1 / (1+3) (√1+1 + √1+1)
=1 / (3) (√2 +√2)
=1 / 6√2
I also got 28 for A
Columbam you got a error on problem B line 3 (x^2+1-x+1) = x^2-x+2
I got 28 for a as well.
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