Application of Derivatives
Find the equation of tangent to the curve given byx=asin3t,y=bcos3t ... (1)at a point where t=2π.
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Find the values of p
If the function f(x)=x3−6x2+ax+b
defined on [1,3] satisfies Rolles theorem for c=323+1
then find the value of aandb
be continuous on [a,b],a>0,and
differentiable on (a,b)˙
Prove that there exists c∈(a,b)
In the curve xm+n=am−ny2n
, prove that the mth
power of the sub-tangent varies as the nth
power of the sub-normal.
The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.
If the curves ay+x2=7andx3=y
cut orthogonally at (1,1)
, then find the value a˙
Discuss the extremum of f(x)=asecx+bcosecx,0<a<b
The acute angle between the curves y=∣∣x2−1∣∣and y=∣∣x2−3∣∣ at their points of intersection when when x> 0, is