Let f(x)=x+1, where a S = (-1, +0). (a) Is the set S open or...

 

Transcribed Image Text:

Let f(x)=√x+1, where a € S = (-1, +∞0). (a) Is the set S open or closed or both or neither? Is S bounded or unbounded? Is S convex or non-convex? What is the interior of S? (Note: No steps are required for (a).) (b) Determine the third-order Taylor series expansion of f(x) about c = 0, namely P3(x), and the truncation error associated with the expansion, namely R3(x). (c) Approximate f(1) by the third-order Taylor series expansion of f(x) about c = 0. How many significant figures do that approximation have? (d) Is f(x) (strictly) convex, (strictly) concave, both convex and concave, or neither convex nor concave over S? Let f(x)=√x+1, where a € S = (-1, +∞0). (a) Is the set S open or closed or both or neither? Is S bounded or unbounded? Is S convex or non-convex? What is the interior of S? (Note: No steps are required for (a).) (b) Determine the third-order Taylor series expansion of f(x) about c = 0, namely P3(x), and the truncation error associated with the expansion, namely R3(x). (c) Approximate f(1) by the third-order Taylor series expansion of f(x) about c = 0. How many significant figures do that approximation have? (d) Is f(x) (strictly) convex, (strictly) concave, both convex and concave, or neither convex nor concave over S?

Answer rating: 100% (QA)

a S is rightopen leftclosed and is thus neither open nor closed S is unbounded sin... View the full answer