Continuity and Differentiability
Find dxdyif x−y=π
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The general solution of the D.E. xdxdy=x2+xy+y2 is:
Show that the function f defined by f(x)=∣1−x+x∣, where x is any real number, is a continuous function.
If x and y are connected parametrically by the equations given, without eliminating the parameter, Find dxdy.x=acosθ,y=bcosθ
If f(x)=∣x∣3, show that fx exists for all real x and find it.
Differentiate w.r.t. x the function cos(acosx+bsinx), for some constant a and b.
Find the general solution for the following differential equation.ydx−(x+2y2)dy=0
Find the general solution of each of the following differential equations:(xcosxy)dxdy=(ycosxy)+x
Differentiate w.r.t. x the function 2x+7cos−1(2x) , −2<x<2