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Derivatives
The rate of change in the value of a function is useful to study the behavior of a function. This change in y for a unit change in x is referred to as the derivative of y with respect to x. In finance and economics, the rate of change is called marginal or incremental. For example, the marginal cost of capital is the rate of change of the total cost of capital per unit change in the new capital raised.
The idea of the deravative as the rate of change of the function at a fixed point has a geometrical foundation. The slope of the tangent to the function at a point equals the derivative at that point.
The derivative is usually denoted by d/dx of f(x) or df/dx . It may be noted that the derivative itself is a function, and the value of the derivative depends upon where it is evaluated.
The derivative of a function f(x) at point 'a' is defined as:
The process of getting the derivatives is called 'differentiating' a function.
methods of interpolation
make an assignment based on congruence of triangle
1. Sketch the Spiral of Archimedes: r= aθ (a>0) ? 2: Sketch the hyperbolic Spiral: rθ = a (a>0) ? 3: Sketch the equiangular spiral: r=ae θ (a>0) ?
real numbers?
1. Let S be the set of all nonzero real numbers. That is, S = R - {0}. Consider the relation R on S given by xRy iff xy > 0. (a) Prove that R is an equivalence relation on S, an
Indefinite Integrals : In the past two chapters we've been given a function, f ( x ) , and asking what the derivative of this function was. Beginning with this section we are now
(x^2+x+3)^4
The first particular case of first order differential equations which we will seem is the linear first order differential equation. In this section, unlike many of the first order
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