Saturday, October 19, 2019

calculus - How to calculate limit?


I'm puzzled with this limit. The answer is -0.5, but how to get it? limx1x+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.


limx1x+x3x+3=limxx3x+3(x1)2x3x+3+x1=limxx2+5x3(x+3)(x3+x+3(x1)x+3)=limxx2+5x3x4+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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