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Linear Approximations
In this section we will look at an application not of derivatives but of the tangent line to a function. Certainly, to get the tangent line we do have to take derivatives, thus in some way this is an application of derivatives as well.
Given a function, f ( x ) , we can determine its tangent at x = a . The equation of the tangent line, that we'll call L ( x ) for this discussion, is,
L ( x ) = f ( a ) + f ′ ( a ) ( x - a )
Take a look at the given graph of a function & its tangent line.
From the graph we can illustrates that near x = a the tangent line & the function have closely the similar graph. On instance we will utilizes the tangent line, L ( x ) , as an approximation to the function, f ( x ) , near x = a . In these cases we call the tangent line the linear approximation to the function at x = a .
Scalar Multiplication - Vector arithmetic Another arithmetic operation that we wish to look at is scalar multiplication. Specified the vector a → = (a 1 , a 2 , a 3 ) and any
In this section we will see the first method which can be used to find an exact solution to a nonhomogeneous differential equation. y′′ + p (t ) y′ + q (t ) y = g (t) One of
4.2^2x+1-9.2^x+1=0
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i need help in discrete mathematics on sets, relations, and functions.
Cylindrical Coordinates - Three Dimensional Space Since with two dimensional space the standard (x, y, z) coordinate system is known as the Cartesian coordinate system. In the
Thomas is remaining track of the rainfall in the month of May for his science project. The first day, 2.6 cm of rain fell. On the second day, 3.4 cm fell. On the third day, 2.1 cm
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