Continuity and Differentiability
Find the derivative of f given by f(x)=sin−1xassuming it exists.
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Find the general solution of each of the following differential equations:dxdy=1+cosx1−cosx.
Solve (1+y2)dx+(x−e−tan−1y)dy=0, given that when y=0, then x=0.
Find the general solution of each of the following differential equations:ydx+(1+x2)tan−1x dy=0.
Differentiate the following w.r.t x.(i) 3x+2+(2x2+41) (ii) esec2(x)+3cos−1(x) (iii) log7(logx)
Verify Mean Value Theorem, if f(x)=x3−5x2−3x in the interval [a, b], where a=1andb=3. Find all c∈(1,3) for which fprime(c)=0.
Find df/dx if f(x) = (sin x) ^ sin x for all o<x<π.
Find the general solution for the following differential equation.dxdy+(x2+1)4xy+(x2+1)21=0
Find the general solution of the differential equation dxdy+1−x21−y2=0.