2. Consider the three functions: 1 f(x) = = x² - h(x) = a. Verify that f'(x) = g(x) and g'(x) = h(x). b. Prove that g(x)

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2 Consider The Three Functions 1 F X X H X A Verify That F X G X And G X H X B Prove That G X 1 (45.37 KiB) Viewed 36 times

2. Consider the three functions: 1 f(x) = = x² - h(x) = a. Verify that f'(x) = g(x) and g'(x) = h(x). b. Prove that g(x) dx = 2/27 - TT. 7 c. Prove that in the interval 0 ≤ x ≤ 1,0 ≤ g(x) ≤.0032. 22 d. Use Part c to prove that 0 < ²/2 - π < .0032. 213 x6 +x5 4 - 3x³ + 4x − 4arctanx g(x) = x4(1-x)4 1+x² 2x³ (x - 1)³ (3x3³ - x² + 4x − 2) (1+x²)²