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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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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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.
Transcribed Image Text: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.
Expert Solution
Step 1: Step 1

(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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