What is the value of

If $$\lim_{x \to \infty} \left[ \frac{x^2 + 1}{x + 1} - ax - b \right] = 0$$, then (a,b) is ​

$$\lim _{n \rightarrow \infty} \frac{1+2+3+\ldots+n}{n^2}$$​ is equivalent to

​What is the value of $$\lim _{x \rightarrow 12} \frac{x^3-1728}{x-12} ?$$​​

​Compute ​

​$$\lim _{x \rightarrow 4} \frac{\left(x^2-7 x+12\right)}{x-4}$$​​

​$$\text { Find } \lim _{x \rightarrow \frac{\pi}{4}} \frac{\cot ^3 x-\tan x}{\cos \left(x+\frac{\pi}{4}\right)}.$$​​

​$$\text { If } f(16)=16 \text { and } f^{\prime}(16)=5 \text {, then } \lim _{x \rightarrow 16} \frac{\sqrt{f(x)}-4}{\sqrt{x}-4}=\text { ? }$$​​

​$$\text { The value of } \lim _{x \rightarrow \infty}\left(\frac{2 x-1}{2 x+3}\right)^{\frac{x+1}{2}} \text { is: }$$​​

​$$\lim_{\theta \to 0} \frac{1 - \cos{m\theta}}{1 - \cos{n\theta}} = \, ?$$​​