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11th Standard English Medium Maths Subject Differential Calculus - Limits and Continuity Book Back 2 Mark Questions with Solution Part - I

11th Standard

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 20

    2 Marks

    10 x 2 = 20
  1. Calculate \(\lim _{ x\rightarrow0}{|x| } \).

  2. Consider the function f(x) = \(\sqrt{x},x\ge0.\) Does\(lim_{x\rightarrow0}f(x)\) exist?

  3. Evaluate \(lim_{x\rightarrow 2^-}\left\lfloor x \right\rfloor \) and \(lim_{x\rightarrow 2^+}\left\lfloor x \right\rfloor \) .

  4. In problems 1-6, using the table estimate the value of the limit.
    \(lim_{x\rightarrow 2}{x-2\over x^2-x-2}\)

    x 1.9 1.99 1.999 2.001 2.01 2.1
    f(x) 0.344820 0.33444 0.33344 0.333222 0.33222 0.332258
  5. In problem, using the table estimate the value of the limit
    \(lim_{x\rightarrow 0}{sin x\over x}\)

    x -0.1 -0.01 -0.001 0.001 0.01 0.1
    f(x) 0.99833 0.99998 0.99999 0.99999 0.99998 0.99833
  6. In problem, using the table estimate the value of the limit
    \(lim_{x\rightarrow0}{cos x-1\over x}\)

    x -0.1 -0.01 -0.001 0.001 0.01 0.1
    f(x) 0.04995 0.0049999 0.0004999 –0.0004999 –0.004999 –0.04995
  7. Use the graph to find the limits (if it exists). If the limit does not exist, explain why?
    \(lim_{x\rightarrow{1}}sin \pi x\)

  8. Use the graph to find the limits (if it exists). If the limit does not exist, explain why?
    \(lim_{x \rightarrow{\pi\over 2}} tanx\)

  9. If the limit of f(x) as x approaches 2 is 4, can you conclude anything about f(2)? Explain reasoning.

  10. Calculate \(lim_{x\rightarrow3}(x^3-2x+6).\)

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