Application of Derivatives
Show that the altitude of a right circular cone of maximum volume that can be inscribed in a sphere of radius r is 4r/3..
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Prove that there exist exactly two non-similar isosceles triangles ABC
such that tanA+tanB+tanC=100.
In the curve y=ceax
sub-tangent is constant
sub-normal varies as the square of the ordinate
tangent at (x1,y1)
on the curve intersects the x-axis at a distance of (x1−a)
from the origin
equation of the normal at the point where the curve cuts y−aξs
If a>b>0, with the aid of Lagranges mean value theorem, prove that nbn−1(a−b)1.
be a polynomial of odd degree (≥3)
with real coefficients and (a, b) be any point.
Statement 1: There always exists a line passing through (a,b)
and touching the curve y=f(x)
at some point.
Statement 2: A polynomial of odd degree with real coefficients has at least one real root.
Find the angle between the curves x2−3y2=a2andC2:xy3=c
If in a triangle ABC,
the side c
and the angle C
remain constant, while the remaining elements are changed slightly, show that
Separate the intervals of monotonocity for the function
Find the angle of intersection of the curves xy=a2andx2+y2=2a2