What is the value of $\underset{\mathrm{x}\to 0}{\lim }\frac{\sin \left(\mathrm{x}°\right)}{\tan \left(3\mathrm{x}°\right)}$

• $\frac{1}{4}$

• $\frac{1}{3}$

• $\frac{1}{2}$

• 1

What is $\underset{\mathrm{x}\to 0}{\lim }\frac{3^{\mathrm{x}} + 3^{ - \mathrm{x}} - 2}{\mathrm{x}} = ?$

• 0

• - 1

• 1

• limit does not exist

What is the maximum value of $\sin \left(\mathrm{x}\right)\cos \left(\mathrm{x}\right)$ ?

• 2

• 1

• $\frac{1}{2}$

• $2\sqrt{2}$

34.

The value of ordinate of the graph of y = 2 + cos(x) lies in the interval

• [0, 1]

• [0, 3]

• [ - 1, 1]

• [1, 3]

What is $\underset{\mathrm{x}\to 0}{\lim }\frac{\sin \left(\mathrm{x}\right)\log \left(1 - \mathrm{x}\right)}{{\mathrm{x}}^2} = ?$

•  - 1

• Zero

•  - e

• - $\frac{1}{\mathrm{e}}$

If $\underset{\mathrm{x}\to 1}{\lim }\frac{{\mathrm{x}}^4 - 1}{\mathrm{x} - 1} = \underset{\mathrm{x}\to \mathrm{k}}{\lim }\frac{{\mathrm{x}}^3 - {\mathrm{k}}^3}{{\mathrm{x}}^2 - {\mathrm{k}}^2} \mathrm{where} \mathrm{k} \ne 0, \mathrm{then} \mathrm{what} \mathrm{is} \mathrm{the} \mathrm{value} \mathrm{of} \mathrm{k} ?$

• $\frac{2}{3}$

• $\frac{4}{3}$

• $\frac{8}{3}$

• $4$

What is $\underset{\mathrm{x}\to 1}{\lim }\frac{\mathrm{x} + {\mathrm{x}}^2 + {\mathrm{x}}^3 - 3}{\mathrm{x} - 1} = ?$

• 1

• 2

• 3

• 6