Use a power series to approximate the value of the integral 0.01. Round your answer to three decimal places. l'e-x² е dx with an error of less than

If sech x = (√21/5)  , find tanh x.

y" + 100y = sec²(10x) %3D (1) Let C1 and C2 be arbitrary constants. The general solution to the related homogeneous differential equation y" + 100y = 0 is the function y, (x) = C1 41(x)+ C2 Y2(x) = C1 +C2 NOTE: The order in which you enter the answers is important; that is, Cif(x) + C29(x) + C19(x) + C2f(x). (2) The particular solution yp(x) to the differential equation y" + 100y = sec²(10x) is of the form yp(x) = Y1(x) u1(x) + Y½(x) U2(x) where u' (x) = and u, (z) = %3D (3) It follows that u1(x) : and u2(x) = ; thus yp(x) = (4) The most general solution to the non-homogeneous differential equation y" + 100y = sec2²(10x) is y = C1 +C2

Use differentials to approximate to 3 decimal places ( 1.09 ) 1/3