Differential equations are equations containing functions y = f(x), g(x) and derivatives of y with respect to x.

a line when intersect another line or axis two kind of angle form ,as an assumption we take positive side of axis, to define the direction of line we take angle made from all three axis.and we take cos not other trigonometric function like sin,tan because we can define Direction cosines of a line are coefficient of i,j,k of a unit vector along that line.

Area of standard ellipse is given by :πab.

If A and B are symmetric matrices of the same order, then AB + BA is always a symmetric matrix.

⇒f′(1)=−e−1+e−1=0

( since C1 and C2 are identical)

A linear programming problem is one that is concerned with finding the optimal value (maximum or minimum) of a linear function of several variables .

A vector has both magnitude as well as direction.