What is \(\rm \displaystyle\lim_{x\rightarrow 0} \dfrac{\sin x \log (1-x)}{x^2}\)  equal to?

If a differentiable function f(x) satisfies \(\mathop {\lim }\limits_{x \to - 1} \dfrac{f(x)+1}{x^2-1}=-\dfrac{3}{2}\)  then what is  \(\mathop {\lim }\limits_{x \to - 1} f(x)\)  equal to?

What is the value of \(\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin x{}^\circ }{\tan 3x{}^\circ }\) ?

What is \(\mathop {\lim }\limits_{x \to \frac{\pi }{6}} \;\frac{{2{{\sin }^2}x\; + {\rm{\;}}\sin x\; - {\rm{\;}}1}}{{2{{\sin }^2}x\; - {\rm{\;}}3\sin x\; + {\rm{\;}}1}}\) equal to?

What is \(\mathop {\lim }\limits_{x \to 0} \frac{{{e^x} - \;\left( {1 + x} \right)}}{{{x^2}}}\) equal to

If \({\rm{F}}\left( {\rm{x}} \right) = \sqrt {9 - {{\rm{x}}^2}} \) , then what is \(\mathop {\lim }\limits_{{\rm{x}} \to 1} \frac{{{\rm{F}}\left( {\rm{x}} \right) - {\rm{F}}\left( 1 \right)}}{{{\rm{x}} - 1}}\) equal to?

What is \(\mathop {\lim }\limits_{{\rm{x}} \to {0^ + }} {\rm{f}}\left( {\rm{x}} \right)\) equal to?

If $log 2 = 0.3010$ and $log 3 = 0.4771$, then the value of $log 36$ is

The L. C. M. of x² - y², x³ - y³ and x³ - x²y - xy² + y³ is:

The series \(1 + \frac{2}{3} + {\left( {\frac{2}{3}} \right)^2} + ... + {\left( {\frac{2}{3}} \right)^{n - 1}}\) is:

The series \(\sum {\left( {\frac{1}{{np}}} \right)} \) is divergent if