Limit Calculator
Calculate limits step by step
This free calculator will try to find the limit (two-sided or one-sided, including left and right) of the given function at the given point (including infinity), with steps shown.
Different techniques are used to handle limits (including indeterminate forms): limit laws, rewriting and simplifying, L'Hôpital's rule, rationalizing the denominator, taking natural logarithm, etc.
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: $$$\lim_{x \to -\infty} 15 e x=-\infty$$$