Differential Calculus Two Marks Questions

11th Standard

    Reg.No. :
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Business Maths

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)

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