2. Rewrite each of the implications below using all 4 forms: (1) only if, (2) is sufficient, (3) is necessary, (4) implies. a) If a function f is differentiable, then f is continuous. b) If x=-7, then x² = 49.
2. Rewrite each of the implications below using all 4 forms: (1) only if, (2) is sufficient, (3) is necessary, (4) implies. a) If a function f is differentiable, then f is continuous. b) If x=-7, then x² = 49.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) If a function f is differentiable, then f is continuous.
Only if: Only if f is continuous, is f differentiable.
Sufficient: If a function f is differentiable, then it is continuous.
Necessary: For a function f to be differentiable, it is necessary for it to be continuous.
Implies: If a function f is differentiable, it implies that it is continuous
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