In each of Problems 13 through 16, determine the critical point x = xº, and then classify its type and examine its stability by making the transformation x = xº+u. *-(-2) + (-¹) I dx dt
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- Differentiate the function of y = (e4x^2+1)3 in two different ways: i.) by differentiating the function without doing any algebra first ii.) by doing as much algebraic simplification as possible beforehandX+x- L-X+, dt 2 x²-1Below is the graph of y = x^2. Transform is to make it the graph of y = 2(x-4)^2 + 3
- Show directly that the given functions are linearly dependent on the real line. That is, find a nontrivial linear combination of the following functions that vanishes identically. f(x)=5x, g(x)=6x^2, h(x)=6x-24^2 enter the non-trivial linear combination. (36)5x+ ( ) 6x^2+ ( ) (6x-24x^2)=0(a) Write the linear interpolation/ shape functions relevant for the 2D rectangular element shown below identifying the shape function for each node. Use the property that N,(x,)= 5, to derive the functions. For example, at node 1, N = 1, so using the equations of line 23 and line 34, we (x-a)(y-b) may write N = Sımilarly, interpolation function N2 should involve equations of %3D 4ab lines 34 and 14, and so onEvaluate * d. [(2? – 1) (x+ 7)] dx 3x^2 + 14x +1 3x^2 14x + 1 3x^2 14x 1 3x^2 + 14x-1
- If f(x) = x2 and g(x) = -2(x-3)2-4 Identify the stages that transform f(x) onto g(x) Transformation -1 Transformation -2 Transformation -3 Transformation -4What kinds of changes occur in the Coefficients of a Nonbasic Variable when the original model is changed?Find the points of intersection of the graphs of the functions y = x2 + 1 and y = 4x