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Limits of Functions

Limits of Rational Functions


Find the value of

limx2x2+5x+6x+2. \lim_{x \to -2} \frac{x^2+ 5x+6}{x+2}.


limx1x1x+32. \lim_{x \to 1} \frac{x-1}{\sqrt{x+3} -2}.

If limxax3a3x2a2=9,\displaystyle \lim_{x \to a} \frac{x^3-a^3}{x^2-a^2}=9, what is the value of limxax3ax2+a2xa3xa?\lim_{x \to a} \frac{x^3-ax^2+a^2x-a^3}{x-a}?

If a a and bb satisfy

limx0xx+ab=6, \lim_{x \to 0} \frac{x}{\sqrt{x+a} - b} = 6,

what is a+b a+b ?


limx(x2+4x1x). \lim_{x \to \infty} \left( \sqrt{x^2 + 4x - 1} - x \right).


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