If `varphi(x)` is a polynomial function and `varphi^(prime)(x)>varphi(x)AAxgeq1a n dvarphi(1)=0,` then `varphi(x)geq0AAxgeq1` `varphi(x)

If varphi(x) is differentiable function AA x in R and a in R^(+) such that varphi(0)=varphi(2a),varphi(a)=varphi(3a)and varphi(0)!=varphi(a) then show that there is at least one root of equation varphi'(x+a)=varphi'(x)in(0,2a)

If y+x(dy)/(dx)=x(varphi(xy))/(varphi'(xy)) then varphi(xy) is equal to

If f(x)=|x-a|varphi(x), where varphi(x) is continuous function, then (a) f^(prime)(a^+)=varphi(a) (b) f^(prime)(a^-)=-varphi(a) (c) f^(prime)(a^+)=f^(prime)(a^-) (d) none of these

Evaluate: int_(pi/4)^((3pi)/4) varphi/(1-sinvarphi)d varphi

The solution of the differential equation (dy)/(dx)=(y)/(x)+(varphi((y)/(x)))/(varphi'((y)/(x))) is varphi((y)/(x))=kxbx varphi((y)/(x))=kc*varphi((y)/(x))=kyd.y varphi((y)/(x))=k

Let int e^(x){f(x)-f'(x)}dx=varphi(x) .Then int e^(x)f(x)dx is varphi(x)=

Evaluate: int(2sin2varphi-cosvarphi)/(6-cos^2varphi-4\ sinvarphi)\ dvarphi