Cho lim x suy ra 1 ((f(x) - 4) / (x - 1)) = 2. Tính: lim x suy ra 1 f(x)
Cho \(\mathop {\lim }\limits_{x \to 1} \frac{{f\left( x \right) - 4}}{{x - 1}} = 2\). Tính:
\(\mathop {\lim }\limits_{x \to 1} f\left( x \right)\);
Nếu \(\mathop {\lim }\limits_{x \to 1} \left[ {f\left( x \right) - 4} \right] \ne 0\) thì \(\mathop {\lim }\limits_{x \to 1} \frac{{f\left( x \right) - 4}}{{x - 1}} = - \infty \) hoặc \(\mathop {\lim }\limits_{x \to 1} \frac{{f\left( x \right) - 4}}{{x - 1}} = + \infty \).
Điều này mâu thuẫn với giả thiết \(\mathop {\lim }\limits_{x \to 1} \frac{{f\left( x \right) - 4}}{{x - 1}} = 2\).
Do vậy \(\mathop {\lim }\limits_{x \to 1} \left[ {f\left( x \right) - 4} \right] = 0\). Suy ra \(\mathop {\lim }\limits_{x \to 1} f\left( x \right) = 4\).