PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions for Mathematics

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). 

Mark the correct alternative in of the following:

Let f(x) = x − [x], x ∈ R, then \[f'\left( \frac{1}{2} \right)\]

Mark the correct alternative in of the following: 

If \[f\left( x \right) = \frac{x - 4}{2\sqrt{x}}\]

Mark the correct alternative in of the following:

If\[y = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + . . .\]then \[\frac{dy}{dx} =\] 

Mark the correct alternative in  of the following:

If\[f\left( x \right) = 1 - x + x^2 - x^3 + . . . - x^{99} + x^{100}\]then \[f'\left( 1 \right)\] 

Mark the correct alternative in  of the following: 

If \[y = \frac{1 + \frac{1}{x^2}}{1 - \frac{1}{x^2}}\] then \[\frac{dy}{dx} =\] 

Mark the correct alternative in of the following:

If \[y = \sqrt{x} + \frac{1}{\sqrt{x}}\] then \[\frac{dy}{dx}\] at x = 1 is

Mark the correct alternative in of the following:
If \[f\left( x \right) = x^{100} + x^{99} + . . . + x + 1\]  then \[f'\left( 1 \right)\] is equal to 

Mark the correct alternative in  of the following:
If\[f\left( x \right) = 1 + x + \frac{x^2}{2} + . . . + \frac{x^{100}}{100}\] then \[f'\left( 1 \right)\] is equal to 

Mark the correct alternative in each of the following:
If\[y = \frac{\sin x + \cos x}{\sin x - \cos x}\] then \[\frac{dy}{dx}\]at x = 0 is 

Mark the correct alternative in  of the following:
If \[y = \frac{\sin\left( x + 9 \right)}{\cos x}\] then \[\frac{dy}{dx}\] at x = 0 is 

Mark the correct alternative in each of the following: 

If\[f\left( x \right) = \frac{x^n - a^n}{x - a}\] then \[f'\left( a \right)\] 

Mark the correct alternative in of the following: 

If f(x) = x sinx, then \[f'\left( \frac{\pi}{2} \right) =\]