Questão de Matemática

EŽĞƐƚƵĚŽĚĞĨƵŶĕƁĞƐĚĞǀĂƌŝĄǀĞŝƐƌĞĂŝƐ͕ďƵƐĐĂŵͲƐĞ ŝŶĨŽƌŵĂĕƁĞƐƐŽďƌĞĐŽŶƟŶƵŝĚĂĚĞ͕ĚŝĨĞƌĞŶĐŝĂďŝůŝĚĂĚĞ͕ ĞŶƚƌĞŽƵƚƌĂƐ͘ŽŶƐŝĚĞƌĞƵŵĂĨƵŶĕĆŽĚĞĚƵĂƐǀĂƌŝĄǀĞŝƐ f͗ R2 R o ͕ĚĞĮŶŝĚĂƉŽƌ ⎧ x2y2 ⎪⎪ ⎨ , se (x, y) = (0, 0) x4 + y4 f(x, y) = ⎪⎪ ⎩ 0, se (x, y) = (0, 0). ƌĞƐƉĞŝƚŽĚĞƐƐĂĨƵŶĕĆŽ͕ĂǀĂůŝĞĂƐĂĮƌŵĂĕƁĞƐĂƐĞŐƵŝƌ͘ /͘ ŽůŽŶŐŽĚĂƐƌĞƚĂƐ y = cx͕ŽǀĂůŽƌĚĂĨƵŶĕĆŽ fĠĐŽŶƐƚĂŶƚĞ͘ //͘ ĨƵŶĕĆŽ fĠĚĞƐĐŽŶơŶƵĂĞŵ(0, 0). 1 ///͘ ĨƵŶĕĆŽ fƐĂƟƐĨĂnj |f (x, y)| < ͕ƋƵĂŝƐƋƵĞƌ 2 2 ƋƵĞƐĞũĂŵ(x, y)  R ͕ĐŽŵ x z y. ĐŽƌƌĞƚŽŽƋƵĞƐĞĂĮƌŵĂĞŵ