Limits

What is $\lim\limits_{x\to0}\dfrac{10^{\sin x}-1}{\tan x}$ equal to ?

What is $\lim\limits_{x\to1}\dfrac{x^{(n^2-1)}-1}{x^{(n+1)}-1}$ equal to, where $n>1$ is a natural number ?

Consider the following for the two (02) items that follow: Let the function $f(x) = x^2 + 9$. What is $\lim_{x \to 0} \dfrac{\sqrt{f(x)} - 3}{\sqrt{f(x)+7} - 4}$ equal to?

What is $\lim _{x \rightarrow 0} \frac{x}{\sqrt{1-\cos ^4 x}}$ equal to?

Let $f(x)=|x|$ and $g(x)=[x]-1$, where [.] is the greatest integer function. Let $h(x)=\frac{f(g(x))}{g(f(x))}$. What is $\lim _{x \rightarrow 0+} h(x)$ equal to?

For the following two (02) items: Let $f(x) = \begin{cases} \dfrac{1 - \cos 2x}{x^2}, & x 0 \end{cases}$ What is $\lim_{x \to 0^+} f(x)$ equal to?

Paragraph : Consider the function $f(x)=\frac{1-\sin x}{(\pi-2 x)^2}$, where $x \neq \frac{\pi}{2}$ and $f\left(\frac{\pi}{2}\right)=\lambda$. Question : What is $\lim _{x \rightarrow \frac{\pi}{2}} f(x)$ equal to?

Let $f(x) \quad \frac{a^{x-1} b^{x-1}}{}$ and $g(x)=x-1$. What is $\lim _{x \rightarrow 1} f(x)^{\frac{1}{g(x)}}$ equal to?

What is $\lim _{x \rightarrow 0} \frac{x}{\sqrt{1-\cos x}}$ equal to?

What is $\lim _{x \rightarrow 2} \frac{2-x}{x^3-8}$ equal to?

Consider the following for the two (02) items that follow: Let the function $f(x) = \sin[x]$, where $[\cdot]$ is the greatest integer function and $g(x) = |x|$. What is $\lim_{x \to 0} \dfrac{f(x)}{g(x)}$ equal to?

What is $\lim _{x \rightarrow 0} \frac{2(1-\cos x)}{x^2}$ equal to?