I'm puzzled with this limit. The answer is -0.5, but how to get it? limx→∞1−x+√x3x+3
Answer
I've tried to multiply by conjugate not only part with a variable, but all the expression, and this way I calculate it without replace and L'Hospital's Rule.
limx→∞1−x+√x3x+3=limx→∞x3x+3−(x−1)2√x3x+3+x−1=limx→∞−x2+5x−3(x+3)(√x3+√x+3(x−1)√x+3)=limx→∞−x2+5x−3√x4+3x3+(x+3)(x+1)
Now we can see easily that factor before x2 is −1 in numerator and 2 in denominator, so the result is −12
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