Application of Derivatives
Let f:(0,∞)R be given by f(x)=∫x1xte−(t+t1)dt, then (a)f(x) is monotonically increasing on [1,∞)(b)f(x) is monotonically decreasing on (0,1)(c)f(2x) is an odd function of x on R
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Using Lagranges mean value theorem, prove that ∣cosa−cosb∣≤∣a−b∣˙
Discuss the extremum of f(x)=sinx+21sin2x+31sin3x,0≤x≤π˙
be a curve defined by y=ea+bx2˙
The curve C
passes through the point P(1,1)
and the slope of the tangent at P
Then the value of 2a−3b
Discuss the extremum of
If the curve C
in the xy
plane has the equation x2+xy+y2=1,
then the fourth power of the greatest distance of a point on C
from the origin is___.
A horse runs along a circle with a speed of 20km/h
. A lantern is at the centre of the circle. A fence is along the tangent to the circle at the point at which the horse starts. Find the speed with which the shadow of the horse moves along the fence at the moment when it covers 1/8 of the circle in km/h.
Find the length of normal to the curve x=a(θ+sinθ),y=a(1−cosθ)
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.