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11th Standard English Medium Maths Subject Differential Calculus - Limits and Continuity Creative 5 Mark Questions with Solution Part - II

11th Standard

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 25

    5 Marks

    5 x 5 = 25
  1. Evaluate \(\lim _{ x\rightarrow 0 }{ \left[ \frac { 1 }{ x } -\log { \frac { (1+x) }{ { x }^{ 2 } } } \right] } \)

  2. Evaluate \(\lim _{ x\rightarrow 0 }{ \frac { \sqrt { 1-{ x }^{ 2 } } -\sqrt { 1+{ x }^{ 2 } } }{ 2{ x }^{ 2 } } } \)

  3. Evaluate \(\lim _{ x\rightarrow 0 }{ \frac { { 4 }^{ x }-1 }{ \sqrt { 1+x } -1 } } \)

  4. Evaluate \(\lim _{ x\rightarrow \frac { 1 }{ \sqrt { 2 } } }{ \frac { x-\cos { (\sin ^{ -1 }{ (x) } ) } }{ 1-\tan { (\sin ^{ -1 }{ x } ) } } } \)

  5. Determine k, so that  \(f\left( x \right) =\begin{cases} k{ x }^{ 2 },\quad x\le 2 \\ 3,\quad x>2 \end{cases}\) is continuous.

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