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11th Standard English Medium Maths Subject Differential Calculus - Limits and Continuity Creative 3 Mark Questions with Solution Part - I

11th Standard

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 15

    3 Marks

    5 x 3 = 15
  1. Evaluate \(\lim _{ x\rightarrow 1 }{ \frac { \sqrt { { x }^{ 2 }-1 } +\sqrt { x-1 } }{ \sqrt { { x }^{ 2 }-1 } } } if\quad x>1\)

  2. Evaluate \(\lim _{ x\rightarrow 1 }{ \frac { (2x-3)\sqrt { x } -1 }{ { 2x }^{ 2 }+x-3 } } \)

  3. Examine the continuity of \(f\left( x \right) =\begin{cases} \frac { \sin { 2x } }{ \sin { 3x } } \quad if\quad x\neq 0 \\ 2\quad \quad \quad if\quad x=0 \end{cases}at\quad x=0\)

  4. If \(f\left( x \right) =\frac { 2x+3\sin { x } }{ 3x+2\sin { x } } ,\quad x\neq 0\) is continuous at x = 0, then find f(0).

  5. Evaluate \(\underset { x\rightarrow 0 }{ lim } f(x)\) ,where \(f(x)=\{ \begin{matrix} \frac { \left| x \right| }{ 0 } & x\neq 0 \\ 0 & x=0 \end{matrix}\)

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