Question

Find the approximate value of f(3·02), up to 2 places of decimal, where f(x) = 3x² + 5x + 3.

Find the equations of the normal to the curve y = x³+ 2x + 6, which are parallel to line x + 14y + 4 = 0.

Solve the following differential equation : (1 + x²) dy + 2xy dx = cot x dx, (x ≠ 0)

Find the particular solution of the differential equation $(1+e^{2x})d y+(1+y^{2})e^{x}d x=0,$ given that y = 1, when x = 0.

Solve the differential equation: $x\,{\frac{d y}{d x}}\ +y=x\cos x+\sin x,$ given $y\left({\frac{\pi}{2}}\right)=1.$

Find the particular solution of the following differential equation : $x y{\frac{d y}{d x}}\,=(x+2)\,(y+2);y=-1,{\mathrm{when}}\,x=1.$

Find the particular solution of the following differential equation : ${\frac{d y}{d x}}-y=\cos x\ {\mathrm{~for~}}x=0,y=1.$