极限计算器

这个免费计算器会尝试求给定函数在给定点（包括无穷处）的极限（双侧或单侧，包含左极限和右极限），并显示解题步骤。

处理极限（包括未定式）可采用多种技巧：极限法则、重写与化简、洛必达法则、分母有理化、取自然对数等。

Enter a function:

Choose a variable:

Find the limit at:

If you need `oo`, type inf.

Choose a direction:

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Solution

Your input: find $$$\lim_{x \to -\infty} 15 e x$$$

Apply the constant multiple rule $$$\lim_{x \to -\infty} c f{\left(x \right)} = c \lim_{x \to -\infty} f{\left(x \right)}$$$ with $$$c=15 e$$$ and $$$f{\left(x \right)} = x$$$:

$${\color{red}{\lim_{x \to -\infty} 15 e x}} = {\color{red}{\left(15 e \lim_{x \to -\infty} x\right)}}$$

The function decreases without a bound:

$$\lim_{x \to -\infty} x = -\infty$$

Therefore,

$$\lim_{x \to -\infty} 15 e x = -\infty$$

Answer: $$$\lim_{x \to -\infty} 15 e x=-\infty$$$

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逐步求极限

Solution