Find the limits: lim_{xrightarrow-2}frac{x+2}{sqrt{x^2+5}-3}

UkusakazaL 2021-03-09 Answered
Find the limits:
limx2x+2x2+53
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Expert Answer

nitruraviX
Answered 2021-03-10 Author has 101 answers

Given limits:
limx2x+2x2+53
Rationalize the denominator, we get
limx2x+2x2+53×x2+5+3x2+5+3
limx2(x+2)(x2+5+3)(x2+5)232
limx2(x+2)(x2+5+3)x2+59
limx2(x+2)(x2+5+3)x24
limx2(x+2)(x2+5+3)x222
limx2(x+2)(x2+5+3)(x2)(x+2)
limx2(x2+5+3)(x2)
Apply the limits x=2, we get
limx2(x2+5+3)(x2)=((2)2+5+3(22)
limx2(x2+5+3)(x2)=(4+5+3(22)
limx2(x2+5+3)(x2)=(3+3)(22)
limx2(x2+5+3)(x2)=32

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