#### Important Questions 5m-Differential Calculus

11th Standard

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Maths

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

Part A

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