Use euler's method to obtain a four-decimal approximation of the indicated value. first use h = 0.1 and then use h = 0.05. find an explicit solution for the initial-value problem and then fill in the following tables. (round your answers to four decimal places. percentages may be rounded to two decimal places. use the rounded values for subsequent calculations.) y' = y, y(0) = 1; y(1.0) y(x) = (explicit solution)

The figure shows the front side of a metal desk in the shape of a trapezoid. what is the area of this trapezoid? 10 ft²16 ft²32 ft²61 ft²

Evaluate 8x2 + 9x − 1 2x3 + 3x2 − 2x dx. solution since the degree of the numerator is less than the degree of the denominator, we don't need to divide. we factor the denominator as 2x3 + 3x2 − 2x = x(2x2 + 3x − 2) = x(2x − 1)(x + 2). since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the form† 8x2 + 9x − 1 x(2x − 1)(x + 2) = correct: your answer is correct. to determine the values of a, b, and c, we multiply both sides of this equation by the product of the denominators, x(2x − 1)(x + 2), obtaining 8x2 + 9x − 1 = a correct: your answer is correct. (x + 2) + bx(x + 2) + cx(2x − 1).

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