Solution for Find the equation of a tangent line to a curve given by f(x) = 3x3 + 2x2 +x+1at x =1.
A formula expressing the Laguerre coefficients of a general-order derivative of an infinitely differentiable function in terms of its original coefficients is proved, and a formula expressing explicitly the derivatives of Laguerre polynomials of any degree and for any order as a linear combination of suitable Laguerre polynomials is deduced.
By contradiction, suppose that the Wronskian W of this set of functions is not identically zero but the functions are linearly dependant. By the theorem about linearly independent sets this means that there exist numbers a1,...,an, not all equal to zero and such that.
Thus the physical law is translated into a differential equation. If we are given FIGURE 1.1.1. Newton's law of the values of k and A, we should be able to find an explicit formula for T(t), and cooling, Eq. (3), describes the then-with the aid of this formula-we can predict the future temperature of the cooling of a hot rock in water. body.
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