Nội dung bài giảng
Bài 48. Tìm các giới hạn sau:
a) \(\mathop {\lim }\limits_{x \to 0} {{{e^2} - {e^{3x + 2}}} \over x}\)
b) \(\mathop {\lim }\limits_{x \to 0} {{{e^{2x}} - {e^{5x}}} \over x}\)
Giải
a) \(\mathop {\lim }\limits_{x \to 0} {{{e^2} - {e^{3x + 2}}} \over x} = \mathop {\lim }\limits_{x \to 0} {{{e^2}\left( {1 - {3^{3x}}} \right)} \over x} = - 3{e^2}.\mathop {\lim }\limits_{x \to 0} {{{e^{3x}} - 1} \over {3x}} = - 3{e^2}\).
b) \(\mathop {\lim }\limits_{x \to 0} {{{e^{2x}} - {e^{5x}}} \over x} = \mathop {\lim }\limits_{x \to 0} \left( {{{{e^{2x}} - 1} \over x} - {{{e^{5x}} - 1} \over x}} \right) = 2 - 5 = - 3\).