PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions

\[\frac{\sec x - 1}{\sec x + 1}\] 

\[\frac{x^5 - \cos x}{\sin x}\] 

\[\frac{x + \cos x}{\tan x}\] 

\[\frac{x}{\sin^n x}\]

\[\frac{ax + b}{p x^2 + qx + r}\] 

\[\frac{1}{a x^2 + bx + c}\] 

Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\] 

Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]

If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\] 

If \[\frac{\pi}{2}\] then find \[\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)\]

Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]

Write the value of \[\frac{d}{dx} \left\{ \left( x + \left| x \right| \right) \left| x \right| \right\}\]

Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.

If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\] 

If f (x) = |x| + |x−1|, write the value of \[\frac{d}{dx}\left( f (x) \right)\]

Write the value of \[\frac{d}{dx}\left( \log \left| x \right| \right)\]

If f (1) = 1, f' (1) = 2, then write the value of \[\lim_{x \to 1} \frac{\sqrt{f (x)} - 1}{\sqrt{x} - 1}\] 

Write the derivative of f (x) = 3 |2 + x| at x = −3. 

If |x| < 1 and y = 1 + x + x² + x³ + ..., then write the value of \[\frac{dy}{dx}\] 

If f (x) =  \[\log_{x_2}\]write the value of f' (x).