9780070109100, Chapter 9 5, Problem 2E

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Chapter Problem 2E Step -step solution Step The Maclaurin's series an expansion function which the sum derivatives of the function adds The function 1-x The general the Maclaurin's series follows f(x)= ... (1) Here value function value of the first order derivative of the function at 0 value second order the function f"(0) value of the third order derivative of the function the value of the fourth order derivative function Step The value function Take the order derivative and find value take second derivative the derivative and value equals 0 Again take the third order derivative (derivate the second order derivative) and find Step 6 Lastly take the fourth order derivative (derivate the order and its value Step substitute values equation(1) 24 3x2x1 the first five terms series are Step 8 (b) function given f(x)= 1+x The general form the Maclaurin's series (given) f(0) f(x)= - (2) Here value value of the derivative of the function f*(0) value the second order derivative function at 0 the value of the third order derivative of the the value of the fourth order derivative of the function a Step of 14 The value function f(x)= 1+x 1-0 1+0 Step Take the order derivative and find value at equals 1-x f(x)= 1+x f'(x)= (1+x) Step take second order derivative the first derivative) and value equals 0 Step Again take the third order derivative the second order derivative) and find value Step Lastly take fourth order derivative (derivate the order and its value Step substitute values Thus the first five terms