Recent content by AAQIB IQBAL

Suppose S is an Ideal of a Ring R I want to verify the multiplication operation in the Factor Ring R/S which is (S + a)(S + b) = (S + ab) for this i Need to show that : (S + ab) ≤ (S +a)(S + b) please give me some idea about it IT IS GIVEN AS DEFINITION IN THE BOOK I.N Herstein

why intersection of empty class of sets is the whole space while their union is null set? Book writes that an element will fail to be in the intersection if it fails to be in one of the sets of the class but since there is nothing in the empty class so there is nothing in the empty class that...

thank you, you have provided most satisfactory answer to my problem (especially "... imagine walking along ..."). Now i need to know one thing that can we assume the coefficient of z in the equation of tangent plane is non zero without loss of generality. Actually while deriving the equation i...

For single variable functions derivative means slope of tangent what does it mean for functions of more than one variable. book says that a function is said to be differentiable if: f(x + Δx , y + Δy) - f(x , y) = AΔx + BΔy + ε'ψ(Δx , Δy) + εh(Δx , Δy) WHERE ε, ε' → 0 AS Δx , Δy → 0...

How to determine period of sin and cos functions? I use: sin(x + p) = sin(x) => sin(x + p) - sin(x) = 0 => 2*cos(x+p/2)*sin(p/2) = 0 => either p/2 = k(pi) => p = 2k(pi) or x + p/2 = (2k+1)(pi)/2 => p = (2k+1)(pi) - 2x NOW I DON'T KNOW HOW TO FIND THE SOLUTION WHICH SATISFIES BOTH...

My question is about the nth derivative of e^ax cos(bx+c). Though i can calculate it easily but i am confused at one point. When we calculate the first derivative we put a = r.cos(theta), b = r.sin(theta) (every thing is ok till here) My confusion starts when we use (theta) = tan^-1(b/a) [tan...

I know that Taylors theorem is used to expand f(a+h) in terms of f(a) and its derivatives in the interval (a,a+h), but my question is that can we use it to expand f(a-h) in terms of f(a) and its derivatives over the interval (a-h,a). If yes please give reason.

PROVE mean (X bar) of a continuous distribution is given by: [SIZE="7"] ∫x.f(x)dx {'a' is the lower limit of integration and 'b' is the upper limit}

The necessary and sufficient condition for homomorphisim f of a group G into a group G' with kernel K to be isomorphism of G into G' is that k={e} ... THOUGH I AM ABLE TO PROVE THAT f IS ONE-ONE AND f IS HOMOMORPHISM (in converse part) BUT CAN'T GET ANY IDEA TO PROVE THAT f IS ONTO. PLEASE...

I have studied a fair portion of groups, but couldn't imagine what they are all about. Please help me in this regards.