If $y=5x^2+6x+6$,$x=2$,and $\Delta x=0.001$,then the value of $dy$ is:

The radius of a circular plate is increasing at the rate of $0.01 \text{ cm/sec}$. When the radius is $12 \text{ cm}$,the rate at which the area increases is:

$A$ man of height $2 \ m$ walks at a uniform speed of $5 \ km/hr$ away from a lamp post which is $6 \ m$ high. The rate at which the length of his shadow increases is .......... $km/hr$.

$A$ square plate is contracting at the uniform rate $3 \,cm^2 / sec$. The rate at which the perimeter is decreasing, when the side of the square is $15 \,cm$, is

If a circular iron sheet of radius $30 \, cm$ is heated such that its area increases at the uniform rate of $6\pi \, cm^2/hr$,then the rate (in $cm/hr$) at which the radius of the circular sheet increases is

The side of a square piece is increasing at a rate of $4 \text{ cm/min}$. Find the rate at which the area is increasing when the side is $8 \text{ cm}$ long.