Let f: R R be the continuous function given by sin(x) f(x) for x +...

 

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Let f: R → R be the continuous function given by sin(x) f(x) for x + 0, with f(0) = 1. Consider the partition of 0, T given by P = {to, ..., to} in with t; 6 Compute the upper and lowers sums U(f,P), L(f,P) . Give exact expressions, but also give a decimal approximation -- you may use a calculator. (This will give an estimate for the integral S" f(x)dx.) 11m How does the upper and lower sums change if you replace the partition with P' = PU{ ? 12 Let f: R → R be the continuous function given by sin(x) f(x) for x + 0, with f(0) = 1. Consider the partition of 0, T given by P = {to, ..., to} in with t; 6 Compute the upper and lowers sums U(f,P), L(f,P) . Give exact expressions, but also give a decimal approximation -- you may use a calculator. (This will give an estimate for the integral S" f(x)dx.) 11m How does the upper and lower sums change if you replace the partition with P' = PU{ ? 12