Differential Calculus - Limits and Continuity Book Back Questions

11th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
    6 x 1 = 6
  1. \(lim_{x\rightarrow\infty}{sin \ x \over x} \)

    (a)

    1

    (b)

    0

    (c)

    \(\infty\)

    (d)

    -\(\infty\)

  2. \(lim_{x\rightarrow {\pi/2}}{2x-\pi\over cosx} \)

    (a)

    2

    (b)

    1

    (c)

    -2

    (d)

    0

  3. \(lim_{x \rightarrow \infty}{\sqrt{x^2-1}\over 2x+1}=\)

    (a)

    1

    (b)

    0

    (c)

    -1

    (d)

    \(1\over 2\)

  4. If f(x)=x(-1)\(\left\lfloor 1\over x \right\rfloor \),\(x\le0\),then the value of \(lim_{x\rightarrow 0}f(x)\) is equal to

    (a)

    -1

    (b)

    0

    (c)

    2

    (d)

    4

  5. If f : \(R \rightarrow R\) is defined by f(x)=\(\left\lfloor x-3 \right\rfloor +|x-4|\) for \(x \in R\), then\(lim_{x\rightarrow 3^-}f(x)\) is equal to

    (a)

    -2

    (b)

    -1

    (c)

    0

    (d)

    1

  6. \(lim_{x \rightarrow 0}{e^{tan \ x}-e^x\over tan x-x}=\)

    (a)

    1

    (b)

    e

    (c)

    \({1\over2}\)

    (d)

    0

  7. 5 x 2 = 10
  8. Complete the table using calculator and use the result to estimate the limit.
    \(lim_{x\rightarrow{0}}{\sqrt{x+3}-\sqrt{3}\over x}\)

    x -0.1 -0.01 -0.001 0.001 0.01 0.1
    f(x)            
  9. Calculate \(lim_{x\rightarrow3}(x^3-2x+6).\)

  10. Evaluate the following limits :
    \(lim_{x\rightarrow1}{x^m-1\over x^n-1}\) ,m and n are integers.

  11. Evaluate:\(lim_{x\rightarrow 0}(1+sin x)^{2 cosec x} \)

  12. Evaluate the following limits :\(lim_{x\rightarrow \infty}(1+{1\over x})^{7x} \)

  13. 3 x 3 = 9
  14. Calculate \(\lim _{ x\rightarrow0}{|x| } \).

  15. Use the graph to find the limits (if it exists). If the limit does not exist, explain why?
    \(lim_{x\rightarrow2}f(x)\)

  16. Use the graph to find the limits (if it exists). If the limit does not exist, explain why?
    \(lim_{x\rightarrow{1}}sin \pi x\)

  17. 1 x 5 = 5
  18. Check if \(lim_{x\rightarrow-58}f(x)\)exists or not, where 

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