Submission Instructions: (Important! If you do not follow them, your paper is not graded.)

• Template (Word file)

• One page for each problem (a total of 2 pages). 50 % Penalty if not followed.

• Make a single PDF file. File name: hw_01_doe_john.pdf.

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1. Derive the relationship between the backward difference operator, ~∆ f ≡ f(x) − f(x − h), and the differential operator, D f ≡ f′(x), and numerically obtain f′(1.0) from the table below using all the available information:


2.

f(x) ≡ ⎧ ⎪ ⎨ ⎪ ⎩ x 1 + exp(1/x)     (x ≠ 0) 0     (x = 0).

(a) Is f(x) continuous at x=0 ? State your rationale.
(b) Is f(x) differentiable at x=0 ? State your rationale.