極限計算器

此免費計算器將嘗試在給定點（包括無窮大）求給定函數的極限（雙側或單側，包括左極限與右極限），並顯示計算步驟。

可使用多種技巧來處理極限（包括未定式）：極限定律、改寫與化簡、羅必達法則、分母有理化、取自然對數等。

Enter a function:

Choose a variable:

Find the limit at:

If you need `oo`, type inf.

Choose a direction:

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

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

Please try a new game Rotatly

逐步計算極限

Solution