EXERCISE 8.3

EXERCISE . . Evaluate lim x y g x y → , if the limit exists, where g x y ( , ) = . Evaluate lim x y . If the limit exists. . Let f x y ( , ) = for ( , ) x y ¹ . Show that lim x y f x y . . Evaluate lim x y x e , if the limit exists. . Let g x y x y ( , ) = for ( , ) x y ¹ and g ( , ) (i) Show that lim x y g x y along every line y mx m  . (ii) Show that lim x y g x y k k = + along every parabola y kx k \{ }  . Show that f x y ( , ) = is continuous at every ( , ) x y ∈  . . Let g x y , for x ¹ and g ( , ) = . Show that g is continuous at ( , ) . and and