Calculus_part2(第二部分)《总共两部分》 下载积分: 1500 内容提示: 8 Applications of the Integral short distance ---dsEXAMPLE 9 Define "speed" by short time dt ' It is /($I + (%I. When a ball is thrown straight upward, dx/dt is zero. But the speed is not dy/dt. It is Idyldt...
To fully understand these steps on how to do related rates, let us see the following word problems about associated rates. Example 1: Related Rates Cone Problem A water storage tank is an inverted circular cone with a base radius of 2 meters and a height of 4 meters. If water is being...
An example of initial values for this second-order equation would be y(0)=2y(0)=2 and y′(0)=−1y′(0)=−1. These two initial values together with the differential equation form an initial-value problem. These problems are so named because often the independent variable in the ...
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Example: Integrating a Function Using the Power Rule ∫ √ ( 1 + t ) d t . ∫ 1 4 t ( 1 + t ) d t Show Solution ∫14t(1+t)dt=∫14t1/2(1+t)dt=∫14(t1/2+t3/2)dt. ∫14(t1/2+t3/2)dt=(23t3/2+25t5/2)|14=[23(4)3/2+25(4)5/2]−[23(1)3/2+25(1)5...
Real example: (details you can refer to here)Q: how different my watch is from the clock on the satellite. Time dilation(special relativity): T'=\frac{T}{\sqrt{1-\frac{v^{2}}{c^{2}}} (1-u)^{-\frac{1}{2}}, with u=\frac{v^{2}}{c^{2}} (1-u)^{-\frac{1}{2}}...
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Differential Calculus is concerned with the problems of finding the rate of change of a function with respect to the other variables. To get the optimal solution, derivatives are used to find the maxima and minima values of a function. Differential calculus arises from the study of the limit ...
•A ⊂B :read A is a subset of B ,means every element of A is an element of B .Example:{2,5}⊂{1,2,3,4,5}.•A ∪B :read A union B ,means the set of all elements that are in A or in B .Example:{$,∗,!}∪{α,!, ,17}={$,∗,!,α, ,17}.•A ∩...
Example 1Let f(x)=2x+2f(x)=2x+2 and compute f(x)f(x) as xx takes values closer to 1. We first consider values of xx approaching 1 from the left (x<1x<1). We now consider xx approaching 1 from the right (x>1x>1). In both cases as xx approaches 1, f(x)f(x) ...