Advanced Calculus by Wilson E.B.

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By Wilson E.B.

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Factoring (x Ex. 3 + A x) n xn may be used to advantage.

X2 If BI, x,,, , , n so great that xn +p xn | 2. If xi, x2 is , x,1 , +p \ < a suite approaching a limit, apply the defigiven it must be possible to find a value of values of p. is , show that when nition of a limit to e is e f or all a suite approaching a limit and if yi, x n approaches zero when n becomes infinite, that \y n a limit which is identical with the limit of the x's. y2 show | 3. As the definition of a limit is phrased in values, note the following rules of operation (a) If > a and Ob.

The is total pressure is then 2Jt0g&(D AA or better the limit of that sum. Then P = lim Vw& () dh = f MJ/I& (A) d/t, the depth of the top of the area and & that of the bottom. To evaluate the pressure it is merely necessary to find the breadth & as a function of A and where a is integrate. EXERCISES 1. If 2. k is Show that f I Ja from a to f wdx vdx. "a ^ (x) (x), show T i/- /a (x) < C dx /a < T dx f(x) (x)dx.

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