Differential Calculus - Limits and Continuity Two Marks Questions

11th Standard

    Reg.No. :
  •  
  •  
  •  
  •  
  •  
  •  

Maths

Time : 00:45:00 Hrs
Total Marks : 20
    10 x 2 = 20
  1. 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)            
  2. Complete the table using calculator and use the result to estimate 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)            
  3. Compute \(lim_{x\rightarrow8}(5x)\)

  4. Compute\(lim_{x\rightarrow-2}(-{3\over 2}x)\)

  5. Find the positive integer n so that \(lim_{x\rightarrow 3}{x^n-3^n\over x-3}=27\)

  6. Evaluate \(\lim _{ x\rightarrow a }{ \frac { \sqrt { x } +\sqrt { a } }{ x+a } } \)

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

  8. \(If\lim _{ x\rightarrow 2 }{ \frac { { x }^{ n }-{ 2 }^{ n } }{ x-2 } } =80\quad and\quad n\in N,\quad find\quad n.\)

  9. Evaluate\(\lim _{ x\rightarrow 0 }{ \frac { { a }^{ x }-1 }{ { b }^{ x }-1 } } \)

  10. For what value of k is the function \(f\left( x \right) =\begin{cases} \frac { \sin { 5x } }{ 3x } \quad if\quad x\neq 0 \\ k,\quad \quad \quad if\quad x=0 \end{cases}\) is continuous at x = 0.

*****************************************

TN 11th Standard Maths free Online practice tests

Reviews & Comments about 11th Maths - Differential Calculus - Limits and Continuity Two Marks Questions

Write your Comment