Limits with roots and parameters
Task number: 2979
Depending on the parameters \(m,n\in \mathbb N\) a \(a,b\in\mathbb R\) determine the limits:
Variant 1
\(\displaystyle \lim_{x\to 0} \frac{(1+mx)^n-(1+nx)^m}{x^2} \)
Variant 2
\(\displaystyle \lim_{x\to \infty} \sqrt{(x+a)(x+b)}-x \)
Variant 3
\(\displaystyle \lim_{x\to 0} \frac{\sqrt[n]{1 + x}-1}x \)
Variant 4
\(\displaystyle \lim_{x\to 1} \frac{\sqrt[m]{x}-1}{\sqrt[n]{x}-1} \)
Variant 5
\(\displaystyle \lim_{x\to 0} \frac{\sqrt[m]{1 + ax}-\sqrt[n]{1 + bx}}x \)
