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#### Application of Differential Calculus Five Marks Questions

12th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
10 x 5 = 50
1. For what value of x the tangent of the curve y = x3 − x2 + x − 2 is parallel to the line y = x.

2. Find the equation of the tangent and normal to the Lissajous curve given by x = 2cos3t and y = 3sin 2t, t ∈ R

3. Expand log(1+ x) as a Maclaurin’s series upto 4 non-zero terms for –1 < x ≤ 1.

4. Expand tan x in ascending powers of x upto 5th power for $(-\frac{\pi}{2} <x<\frac{\pi}{2} )$

5. Find the intervals of monotonicity and hence find the local extrema for the function f (x) = x2 − 4x + 4

6. Find the intervals of monotonicity and hence find the local extrema for the function $f(x)=x^{\frac{2}{3}}$.

7. Discuss the monotonicity and local extrema of the function $f(x)=log(1+x)-\frac{x}{1+x},x>-1$ and hence find the domain where, $log(1+x)>\frac{x}{1+x}$

8. Find the intervals of monotonicity and local extrema of the function f (x) = x log x + 3x.

9. Prove that among all the rectangles of the given area square has the least perimeter.

10. Find the points on the unit circle x2 + y2 =1 nearest and farthest from (1,1).