In each of 3 through 6, let 0(t) = 0 and define {n(t)} by the method of successiveapproximations(a) Determine n(t) for an arbitrary value of n.(b) Plot n(t) for n = 1, ... , 4. Observe whether the iterates appear to be converging.(c) Express limn n(t) = (t) in terms of elementary functions; that is, solve the given initialvalue problem.(d) Plot |(t) n(t)| for n = 1, ... , 4. For each of 1(t), ... , 4(t), estimate the interval inwhich it is a reasonably good approximation to the actual solution.y= 2(y + 1), y(0) = 0

Topic=YellowSubtopic=Green Multivariable Calculus and Matrix Algebra Orthogonal Set, Orthonormal Set Definition: a) Suppose u is a subset of nonzero vectors in an inner product space V if u,u=0 whenever I doesn’t equal j we say the u is orthogonal b) Suppose u is an orthogonal set If u=1 for every k then u is called orthonormal set Theorem: an orthogonal set is L.I Theorem: Riess-Fisher Definition: Suppose that u is a linear combination of an orthonormal set Theorem: Suppose T:vw is liner and u,w use finite dimensions. Then nullity(T) + rank(T) = dimV Definition: The rank of matrix is the dimension of the range of A, which is the maximum number of L.I rows Theorem: Let a=Matrix(R) Suppose a) Lambda are the ideal columns of