Application of Derivatives
A stone is dropped into a quiet lake and waves move in circles at a speed of 4cm per second. At the instant, when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing?
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Find the length of normal to the curve x=a(θ+sinθ),y=a(1−cosθ)
Find the values of a
is increasing for all values of x˙
is the latus sectum of the parabola y2=4axandPP′
is a double ordinate drawn between the vertex and the latus rectum. Show that the area of the trapezium PPprimeLL′
is maximum when the distance PP′
from the vertex is a/9.
For the curve y=a1n(x2−a2)
, show that the sum of length of tangent and sub-tangent at any point is proportional to product of coordinates of point of tangency.
are angles satisfying 0<α<θ<β<2π˙
Then prove that
In the curve xayb=Ka+b
, prove that the potion of the tangent intercepted between the coordinate axes is divided at its points of contact into segments which are in a constant ratio. (All the constants being positive).
Discuss the extremum of f(x)=x(x2−4)−31
Discuss the applicability of Rolles theorem for the following functions on the indicated intervals: