limits and derivative class-11

limits and derivative class-11

Multiple Choice

find the derivative of 

 $f\left(x\right)\ =\ \frac{1-\cos x}{1+\cos x}\ and\ then\ find\ f'\left(\frac{\pi}{2}\right)$  

• 1

• 2

• 3

• 4

Multiple Choice

Evaluate :

 $\lim_{x\rightarrow0}\ \frac{\left(x+1\right)^{5^{ }}-1}{x}$  

• 3

• 4

• 5

• 6

Multiple Choice

Evaluate:

 $\lim_{x\rightarrow\ \frac{\pi}{2}\ }\ \frac{\tan2x}{x-\frac{\pi}{2}}$  

• 2

• 3

• 4

• 5

Multiple Choice

Evaluate

• -7
• 0
• 1
• DNE

Multiple Choice

• 1/11

• 15/11

• -1

• -1/11

Multiple Choice

Differentiate y = (x³ - 1)¹⁰⁰

• 300x²(x³ - 1)⁹⁹

• 99(x³ - 1)⁹⁸

• 100(x³ - 1)⁹⁹

• 100(3x²)⁹⁹

Multiple Choice

Differentiate 1/x²

• 1/2x

• -2/x³

• 2x^-1

• -2x^-1

Multiple Choice

Evaluate:

 $\lim x\rightarrow0\ \frac{\cos2x-1}{\cos x-1}$  

• 1

• 2

• 3

• 4

• not define

Multiple Choice

 $f\left(x\right)=\ \frac{\left(1-\tan^2x\right)}{\left(1+\tan^2x\right)}\ \ \ find\ f'\left(\frac{\pi}{4}\right)$  

• -1

• -2

• 1

• 2