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Estimation: Newton's method and areas - Math 1A, section 103
1. Approximate √3 using Newton's method.
2. Try to compute ln(2) without a calculator. In other words, use Newton's method to approximate the solutions of the equation ex - 2 = 0.
3. Approximate π.
4. (a) Find an expression for the area under the curve y = x3 from 0 to 1 as a limit.
(b) Evaluate the limit in part (a). You may use the formula
13 + 23 + 32 + · · · + n3 = (n(n + 1)/2)2.
5. Using the definition of the definite integral in terms of limits of Riemann sums, prove that
a∫b x dx = (b2 - a2)/2.
5. Use the fundamental theorem of calculus to find
-1∫2 x3 - 2x dx.
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