Question

tính \(\lim\limits_{x\rightarrow4}\dfrac{2x^2-13x+20}{x^3-64}\)

Answer 1

\(\lim\limits_{x\rightarrow4}\dfrac{2x^2-13x+20}{x^3-64}\)

\(=\lim\limits_{x\rightarrow4}\dfrac{2x^2-8x-5x+20}{\left(x-4\right)\left(x^2+4x+16\right)}\)

\(=\lim\limits_{x\rightarrow4}\dfrac{\left(x-4\right)\left(2x-5\right)}{\left(x-4\right)\left(x^2+4x+16\right)}\)

\(=\lim\limits_{x\rightarrow4}\dfrac{2x-5}{x^2+4x+16}=\dfrac{2\cdot4-5}{4^2+4\cdot4+16}=\dfrac{3}{48}=\dfrac{1}{16}\)

Answer 2

Lời giải:
\(\lim\limits_{x\to 4}\frac{2x^2-13x+20}{x^3-64}=\lim\limits_{x\to 4}\frac{(2x-4)(x-4)}{(x-4)(x^2+4x+16)}=\lim\limits_{x\to 4}\frac{2x-4}{x^2+4x+16}=\frac{1}{12}\)