1. In an experiment, an ice cube is melting and its volume decrease steadily at rate of 10 cm^3/s .Find the rate of decrease of its suface area when the area of a face is 16 cm^2
2. A stone is dropped into calm water and causes a circular wave moving outward at a rate of 4/5 m/s. Find the rate of increase of the area of the region bounded by the wave when the area is 100π cm^2
3. lim tan4x/(e^3x-e^2x) ,where x trend to 0
linit and differentiation
2011-02-13 10:53 pm
回答 (1)
2011-02-13 11:07 pm
✔ 最佳答案
1 V = x^3 where x is the length of the sidedV/dt = (3x^2)(dx/dt) = 10
A = 6x^2 => dA/dt = (12x)(dx/dt) = (12x)(10/3x^2) = 40/x
When area of a face is 16 cm^2 => x = 4 cm
dA/dt = 10 cm^2/s.
2 dr/dt = 4/5 m/s
A = πr^2 => dA/dt = 2πr(dr/dt) = (8πr/5) m^2/s
When A = 100π m^2, =>r = 10
dA/dt = 16π m^2/s
3. lim(x->0) tan4x/(e^3x-e^2x)
= 4 lim(x->0) (sec4x)^2/(3e^3x-2e^2x)
= 4
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