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Example: Integrating a Function Using the Power Rule ∫ √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)5/2]=25615. ...
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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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. ...
For example, integrating a velocity function yields a distance function, which enables the distance traveled by an object over an interval of time to be calculated. As a result, much of integral calculus deals with the derivation of formulas for finding antiderivatives. The great utility of the...
Learn what optimization means in calculus. Discover the optimization problems. Learn the steps to solve the optimization problems. See optimization...
As a simple example, let’s take 3/2. Subtract a multiple of the denominator from the numerator.The denominator: the denominator (bottom number) is 2, so multiples of 2 are 2, 4, 6, 8…; The biggest multiple of 2 we can subtract from the numerator is just 2 · 1 = 2. ...
Taylor’s Theorem: Definite, Step by Step Example See also:Sequence and series(main page) Volume: Volume of a Cone Volume of an Egg Cylindrical Shell Formula Washer Method Word Problems Index TI 89 Calculus: Step by Step The Tautochrone Problem / Brachistrone Problem ...
Don’t forget to factor x2−2x−3x2−2x−3 before getting a common denominator. Let’s now revisit one-sided limits. Simple modifications in the limit laws allow us to apply them to one-sided limits. For example, to apply the limit laws to a limit of the form limx→a−h(...