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Differentials with more than two variables Write the differential dw in terms of the differentials of the independent variables.
41.
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Calculus: Early Transcendentals (3rd Edition)
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Precalculus
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- Blood Pressure The rate of change of the volume V(t) of blood in the aorta at time t is given by V(t)=kP(t), where P(t) is the pressure in the aorta at time t and k is a constant that depends upon properties of the aorta. The pressure in the aorta is given by P(t)=P0emt, where P0 is the pressure at time t=0 and m is another constant. Letting V0 be the volume at time t=0, find a formula for V(t).arrow_forwardPlant Growth Researchers have found that the probability P that a plant will grow to radius R can be described by the differential equation dPdR=4DRP2 where D is the density of the plants in an area. Source: Ecology. Given the initial condition P(0)=1, find a formula for P in term of R.arrow_forwardCalculate the differential of y = dy The value of dy when help (formulas) = 10x³ + 6 √x+6 2 and da = Evaluate the differential when x = 2 and da = 0.005. 0.005 is help (numbers)arrow_forward
- Using differentials, determine the appropriate increase in the volume of a sphere if the radius increases from 5 cm to 5.05 cm. O a. 539.5 cm3 O b.47.1 cm3 O . 15.7 cm3 Od.314.2 cm3arrow_forwardFind the differential of f(x,y)=sqrt(x2+y2+144) at the point (3,4). df= _________ Then use the differential to estimate f(3.02,3.94). f(3.02,3.94)≈ ________________________arrow_forward
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