# CBSE Class 12-science Maths Rate of Change and Approximations

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- A ladder 17 metre long is leaning against the wall. The base of the ladder is pulled away from the wall at a rate of 5m/s. When the base of the ladder is 8 metres from the wall, i) How fast is the top of the ladder moving down the wall? ii) At what rate, the area of the triangle formed by the ladder, wall, and the floor, is changing ?
- Using differentials find the approx value
Log
_{e}10.02 given that log_{e}10 = 2.3026 - Using differentials find the approx value
(27)
^{1/3} - Find the value of approximately using differentials.
- The total revenue obtained by selling x units of a commodity is given by
R(x) = 12x
^{2}- 24x +19. Find the marginal revenue when x=17. - Find the approximate value of f(4.02) where the function is given by
f(x)=x
^{3 }- 3x^{2 }+ x + 2 - A ladder, which is 13 m in length, is resting against a wall. A man starts pulling the foot of the ladder away from the wall at the rate of 3 m/s. Find the rate at which the top of the ladder is sliding when the foot of the ladder is 5 m away from the wall.
- Look at the conical funnel whose vertical angle is 90
^{o}. Water is dripping out from it at uniformly at the rate of 8 cm^{3}/sec through a tiny hole at the vertex. Find the rate at which the slant height of the water is decreasing when the slant height of the water is 4cm. Is leaking of water leads to wastage of water? Do you think we can afford to waste our natural resources? - A girl whose height is 160 cm is walking with a speed of 4 m/min away from a lamppost, which is 6.4 m high. Now, her shadow is being formed which is increasing as she moves away. Find out the rate at which the shadow is increasing.
- Find using differentials.

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