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6. Choose and work either (a) or (b), NỘT BOTH. (a) Let f: R? prove that f is continuous at (1, –1). R² be defined by f(x,y) = (x + y, x – y). Use the definition to

6. Choose and work either (a) or (b), NỘT BOTH. (a) Let f: R? prove that f is continuous at (1, –1). R² be defined by f(x,y) = (x + y, x – y). Use the definition to

Advanced Engineering Mathematics
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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Real Analysis 1- Using the 2nd photo solution as an example, solve similarly the problem 6A

6. Choose and work either (a) or (b), NOT BOTH. (a) Let f : R? → R? be defined by f(x, y) = (x+ y,x – y). Use the definition to prove that f is continuous at (1, –1). (b) Use the Mean Value Theorem on the interval [0, x] for x > 0, to show that In(1+x) < x.
Transcribed Image Text:6. Choose and work either (a) or (b), NOT BOTH. (a) Let f : R? → R? be defined by f(x, y) = (x+ y,x – y). Use the definition to prove that f is continuous at (1, –1). (b) Use the Mean Value Theorem on the interval [0, x] for x > 0, to show that In(1+x) < x.
2. fiR?-2 given hy fray)= (x-2y, xy) s continuos ur 6,). side work:ll fam)-fo,)= Prof: or E70 be arbidrary. hope dro pulh hat Samin 1, ) hen メー Je-りtなー, than |fs)-f) (x-1) y +G-i) %3D X-2y, Xy t (6-)203¬), *)yr = 7. The defuln reguino Rur c6,)-61,0|| [IK-11+2/9-1 2. 2 98495?=v185?= 325s3 3. = { ニ こ こ :- Cmti nun, at C) o 352
Transcribed Image Text:2. fiR?-2 given hy fray)= (x-2y, xy) s continuos ur 6,). side work:ll fam)-fo,)= Prof: or E70 be arbidrary. hope dro pulh hat Samin 1, ) hen メー Je-りtなー, than |fs)-f) (x-1) y +G-i) %3D X-2y, Xy t (6-)203¬), *)yr = 7. The defuln reguino Rur c6,)-61,0|| [IK-11+2/9-1 2. 2 98495?=v185?= 325s3 3. = { ニ こ こ :- Cmti nun, at C) o 352
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