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...
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 ...
9. Newton’smethod: y=f’(x1)(x-x1)+f(x1). It is normally used to find a zero for na function but sometimes people use it to estimate y values. For example, when we known f(0), f’(0), we can estimate f(0.1) by f(0.1)=f’(0)*(0.1-0)+f(0) 10. Related rates pro...
1.a method of calculation, esp. one of several highly systematic methods of treating problems by a special system of algebraic notations, as differential or integral calculus. 2.a stone, or concretion, formed in the gallbladder, kidney, or other part of the body. ...
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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...
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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 ...
Learn to solve different kinds of related rate problems in calculus. This article is a full guide that shows the step-by-step procedure for solving problems involving related/associated rates. Includes 11 examples.
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) ...