" /> -->

Differential Calculus Three Marks Questions

11th Standard

Reg.No. :
•
•
•
•
•
•

Time : 01:00:00 Hrs
Total Marks : 30
10 x 3 = 30
1. If $y=\sqrt { x } +\frac { 1 }{ \sqrt { x } }$ show that $2x\frac { dy }{ dx } +y=2\sqrt { x }$.

2. Show that the function f(x) = [x] where [x] denotes the greatest integer function is discontinuous at all integral points

3. Is the function defined by f(x) = x2 -sin x + 5 is continuous at x =$\pi$?

4. Differentiate: $\sin ^{ -1 }{ \left( \sqrt { \cos { x } } \right) }$

5. Differentiate: sin2 x + cos2 y = 1.

6. Differentiate: sin x.sin 2x. sin 3x with respect to 'x'.

7. Find $\frac{dy}{dx}$ if x = 15(t - sin t); y = 18(1 - cos t).

8. If ey (x + 1) = 1, show that $\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } ={ \left( \frac { dy }{ dx } \right) }^{ 2 }$

9. Evaluate $\underset { x\rightarrow -3 }{ lim } \frac { { x }^{ 3 }+27 }{ { x }^{ 5 }+243 }$

10. Evaluate $\underset { x\rightarrow 0 }{ lim } \frac { 2sinx-sin2x }{ { x }^{ 3 } }$