CBSE Guess > Papers > Important Questions > Class XII > 2011 > Maths > Maths By Mrs. E.Praveen

CBSE CLASS XII

Differentiability Applications (4 Mark)

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21. A ladder 5m. long is leaning against a wall . The bottom of the ladder is pulled along the ground, away from the wall at the rate of 2 m./sec. How fast is its height decreasing on the wall,when the foot of the ladder is 4 m away from the wall.
22. Show that the function f given by f(x) = tan^-1(sinx+cosx), is strictly decreasing function on (π/4,π/2)
23. Find the equation of the tangents to the curve y = √3x-2 which is parallel to the line 4x-2y+5=0.
24. Find the intervals in which the function f(x) = x³+1/ x³ increasing or decreasing.
25. Verify Rolle’s theorem for the function f(x)=x³+2x-8 ,
26. Find the equation of the tangent and normal to the parabola y² = 4 a x at ( at², 2at).
27. Using LMVT, find a point on the parabola y = ( x – 3 )² , where the tangent is parallel to the chord (3,0) and (4,1).
28. Verify Rolle’s theorem for f (x) = x³- 2x²- x + 3 in [0,1] .
29. Find the intervals in which f(x) = x³+ 2x²–1 decreasing or increasing
30. It is given for the function of defines by f(x)=x³+ bx²–ax, Rolle’ theorem helds with
31. Find the intervals in which f(x) = - 2 x³+15x²- 36x + 1 is increasing or decreasing.
32. Show that the parabola y² = 4 x + 4 & y² = 4 - 4 x intersect at right angle.
33. Find the interval in which the function f is given by f(x)=sinx-cosx,o ≤ x ≤ 2 π
    (i) Increasing
    (ii) Decreasing.
34. It is given that for the function f given by f(x)=x³+ bx²–axRolle’s theorem hold .Find the values of a and b
35. Find the equation of the tangent and normal to the curve: x = acost +at sint , y = asint - atcot at any point ‘t’. Also show that the normal to the Curve is at a constants distance from the origin.
36. Using differentiate find approximate value of √51.
37. The surface area of a spherical bubble is increasing at the rate of 2m²/sec. Find the rate of at which the volume of the bubble is increasing at the instant its radius is 6cm.
38. Prove that x/a + y/b = 1 is a tangent to the curve y = be^-x/a at the point where the curve cuts y-axis.
39. Find the equation of the tangent to the curve x² + 3y – 3 = 0, which is perpendicular to the line y = 4x – 5.
40. Find the approximate change in the volume V of cube of side x mts caused by increasing the side 2 %.

 

Submitted By Mrs. E.Praveen
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