Important Questions 5m-Differential Calculus

11th Standard

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Maths

Time : 00:50:00 Hrs
Total Marks : 50

    Part A

    Answer all the questions

    10 x 5 = 50
  1. Check if \(lim_{x\rightarrow-58}f(x)\)exists or not, where 

  2. Evaluate the following limits :
    \(lim_{x\rightarrow5}{\sqrt{x-1}-2\over x-5}\)

  3. Evaluate the following limits :\(lim_{x\rightarrow 0}{\sqrt{1+sin x}-\sqrt{1-sinx}\over tanx}\)

  4. State how continuity is destroyed at x= xofor each of the following graphs.

  5. Find the slope of the tangent line to the graph of f(x) = 7x + 5 at any point (x0, f(x0)).

  6. Differentiate the following: \(y=\sqrt{1+2 \ tan \ x}\)

  7. Find the second order derivative if x and y are given by
    x = a cos t
    y = a sin t.

  8. If \(y={sin^{-1}x\over \sqrt{1-x^2}}\) ,show that (1-x2)y2-3xy1-y=0.

  9. If y = \((cos^{-1}x)^2\) ,prove that \((1-x^2){d^2y\over dx^2}-x{dy\over dx}-2=0.\)  Hence find y2 when x=0

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