Bài 5.34 trang 124 SGK Toán 11 tập 1 - Kết nối tri thức

Ta có:

\(\mathop {\lim }\limits_{x \to {a^ - }} f\left( x \right) = \mathop {\lim }\limits_{x \to {a^ - }} \left( {x + 1} \right) = a + 1\)

\(\mathop {\lim }\limits_{x \to {a^ + }} f\left( x \right) = \mathop {\lim }\limits_{x \to {a^ + }} {x^2} = {a^2}\)

Hàm số liên tục trên \(\mathbb{R}\;\)khi \(\mathop {\lim }\limits_{x \to {a^ - }} f\left( x \right) = \mathop {\lim }\limits_{x \to {a^ + }} f\left( x \right)\)

\( \Leftrightarrow a + 1 = {a^2}\;\)

\( \Leftrightarrow {a^2} - a - 1 = 0\)

                                 \( \Leftrightarrow a = \frac{{1 + \sqrt 5 }}{2}\;,a = \frac{{\left( {1 - \sqrt 5 } \right)}}{2}\)