1. \(\lim_{x \to a} [f(x)g(x)] = \lim_{x \to a} f(x) \times \lim_{x \to a} g(x)\);
2. \(\lim_{x \to a} \dfrac{f(x)}{g(x)} = \dfrac{\lim_{x \to a} f(x)}{\lim_{x \to a} g(x)}\)

1. \(\lim_{\theta \to 0} \frac{\sin\theta}{\theta} = 1\)
2. \(\lim_{\theta \to 0} \frac{\theta}{\sin\theta} = 1\)
3. \(\lim_{\theta \to 0} \frac{\theta}{\tan\theta} = 1\)
4. \(\lim_{\theta \to 0} \frac{\tan\theta}{\theta} = 1\)
5. \(\lim_{x \to 0} (1 + x)^{\frac{1}{x}} = e\)
6. \(\lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^x = e\)
7. \(\lim_{x \to a} \frac{x^n - a^n}{x - a} = n a^{n-1}\)

লিমিট নির্ণয়ে ব্যবহৃত কয়েকটি ধারা

1. \(e = 1 + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \dots\)
2. \(\frac{1}{e} = 1 - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} + \dots\)
3. \(e^x = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots\)
4. \(e^{-x} = 1 - \frac{x}{1!} + \frac{x^2}{2!} - \frac{x^3}{3!} + \dots\)
5. \(a^x = 1 + \frac{x \ln a}{1!} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \dots\)
6. \(\ln(1 + x) = x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \dots\)
7. \(\ln(1 - x) = -x - \frac{x^2}{2} - \frac{x^3}{3} - \frac{x^4}{4} - \dots\)
8. \(\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \dots\)
9. \(\cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \dots\)
10. \(\tan x = x + \frac{x^3}{3} + \frac{2x^5}{15} + \dots\)