Question

$$\mathop {\lim }\limits_{x \to \frac{\pi }{4}} {\left( {2 - \tan \,x} \right)^{\log \,\tan \,x}}$$ is equal to :

A. 0

B. 1

C. $$e$$

D. $${e^{ - 1}}$$

Answer : 1

Solution :
$${\text{Limit}} = {\left( {2 - 1} \right)^{\log \,1}} = {1^0} = 1$$

Releted MCQ Question on
Calculus >> Limits

Releted Question 1

lf $$f\left( x \right) = \sqrt {\frac{{x - \sin \,x}}{{x + {{\cos }^2}x}}} ,$$ then $$\mathop {\lim }\limits_{x\, \to \,\infty } f\left( x \right)$$ is-

A. $$0$$

B. $$\infty $$

C. $$1$$

D. none of these

Releted Question 2

If $$G\left( x \right) = - \sqrt {25 - {x^2}} $$ then $$\mathop {\lim }\limits_{x\, \to \,{\text{I}}} \frac{{G\left( x \right) - G\left( I \right)}}{{x - 1}}$$ has the value-

A. $$\frac{1}{{24}}$$

B. $$\frac{1}{{5}}$$

C. $$ - \sqrt {24} $$

D. none of these

Releted Question 3

$$\mathop {\lim }\limits_{n\, \to \,\infty } \left\{ {\frac{1}{{1 - {n^2}}} + \frac{2}{{1 - {n^2}}} + ..... + \frac{n}{{1 - {n^2}}}} \right\}$$ is equal to-

A. $$0$$

B. $$ - \frac{1}{2}$$

C. $$ \frac{1}{2}$$

D. none of these

Releted Question 4

If $$\eqalign{ & f\left( x \right) = \frac{{\sin \left[ x \right]}}{{\left[ x \right]}},\,\,\left[ x \right] \ne 0 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 0,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[ x \right] = 0 \cr} $$
Where \[\left[ x \right]\] denotes the greatest integer less than or equal to $$x.$$ then $$\mathop {\lim }\limits_{x\, \to \,0} f\left( x \right)$$ equals

A. $$1$$

B. $$0$$

C. $$ - 1$$

D. none of these

Practice More Releted MCQ Question on
Limits