#### Differential Calculus Two Marks Questions

11th Standard

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Time : 00:45:00 Hrs
Total Marks : 20
10 x 2 = 20
1. If $f(x)={ x }^{ 3 }-\frac { 1 }{ { x }^{ 3 } }$ then show that $f(x)+f\left( \frac { 1 }{ x } \right) =0$

2. If $f(x)=\frac { x+1 }{ x-1 }$ ,then prove that f(f(x))=x

3. Find the derivative of the following functions from first principles log (x+1)

4. If $f\left( x \right) =\frac { 1 }{ 2x+1 } ,x\neq -\frac { 1 }{ 2 }$ then show that $f\left( f\left( x \right) \right) =\frac { 2x+1 }{ 2x+3 }$ provided that $x\neq -\frac { 3 }{ 2 }$

5. Show that the function f(x) = 5x -3 is continous at x = +3

6. Evaluate $\underset { h\rightarrow 0 }{ lim } \frac { \sqrt { x+h } -\sqrt { x } }{ h }$

7. Differentiate (sec x -1) (sec x +1)

8. Differentiate $\frac { { x }^{ 2 }cos\frac { \pi }{ 4 } }{ sinx }$

9. If f(x) = log $\frac{1+x}{1-x}$, show that $f(\frac{2x}{1+x^2})=2f(x)$

10. If f(x) = x and and g(x) = |x|, then find (f + g)(x)