(Solution) - Use Newton s method to find solutions accurate to within 10 5 -(2025 Original AI-Free Solution)

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Use Newton's method to find solutions accurate to within 10?5 to the following problems.
a. x2 ? 2xe?x + e?2x = 0, for 0 ? x ? 1
b. cos(x +?2) + x(x/2 + ?2) = 0, for ?2 ? x ? ?1
c. x3 ? 3x2(2?x) + 3x(4?x) ? 8?x = 0, for 0 ? x ? 1
d. e6x + 3(ln 2)2e2x ? (ln 8)e4x ? (ln2)3 = 0, for ?1 ? x ? 0