Application Of Differentiation Application Of Differentiation
Expressions for velocity and acceleration of a particle moving along a curve (curvilinear motion) are more complicated than for a particle moving in a straight line. The equation of the curve can be given in parametric form as x = f(t) and y = g(t), where t represents time. Velocity v is a vector tangent to the curve and has an x and a y component, and is expressed in terms of magnitude (speed) and direction. differentiation is used to find rates of inclination of declination. For example, say you wanted to find the dimensions of a box that would be the largest with a given amount of material. By using differentiation, you can determine what measurements will give the greatest volume - and therefore the greatest size. This form of differentiation is called related rates. Know More About History Of Rational Numbers
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There are several other applications, from harmonics, to physics, to circuitry; and they all are detrimental to the development of modern technologies that the normal civilian society cannot recognize at a first glance. By using these techniques in mathematics, we really are improving things that most people fail to understand. Steps in Solving Optimization Problems 1. Understand the problem. 2. Draw a Diagram. 3. Introduce Notation. Assign a symbol to the quantity that is to be maximized or minimized (say Q). Also select symbols (a, b, c, …, x, y) for other unknown quantities and label the diagram with these symbols. 4. Express Q in terms of some of the other symbols from Step 3. 5. Find the relationship between Q and the unknown quantities. 6. Find the absolute maximum or minimum value of f . + Example A cylindrical can is to be made to hold 1 L of oil. Find the dimensions that will minimize the cost of the metal to manufacture the can. Solution Draw the diagram as in the figure 1 below, where r is the radius and h is the height (both in centimeters). In order to minimize the cost of the metal, we minimize the total surface area of the cylinder (top, bottom, and sides).
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The differentiation is the subfield of calculus and there are various application of differentiation in real world. The differentiation is very important part of math as it is used in many scientific fields. Differentiation can be defined as the process of finding the derivatives of the functions. Differentiation can be used as a tool to calculate or study the rate of change of a quantity with respect to change in some other quantity. The most common example is calculation of velocity and acceleration. Velocity is given by v = dx / dt, where ' x ' is the distance covered by a moving body in time ‘t’. Related rates- When two are varying with respect to time and if they are related, then they can be expressed in terms of each other. We will have to differentiate both sides with respect to time d / dt. Drawing a curve- We can sketch a curve using differentiation, we can find the Maxima and Minima using given data by finding the first derivative that is dy / dx or y ' and putting it equals to 0 that is y ' = 0 if value of ' x ' is positive then function has local minima and otherwise function has a local maxima.
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Published on Apr 17, 2012
Expressions for velocity and acceleration of a particle moving along a curve (curvilinear motion) are more complicated than for a particle m...