6.Show that
7.Determine the path of steepest descent along the surface z = x²+3y² from the point (1,1,4) to the point (0,0,0).
(b) (5%) lim_(n→∞) (3n+4/n)^(1/n) = 4
(a) (5%) lim_(x→0+) √(xlnx) = 0
VI. 閱讀測驗
Jack was walking down the street when he saw a big dog. The dog looked very, very mean. It kept on barking at Jack, so Jack stopped walking. Jack saw a woman standing near the dog, so he walked up to her and said, "Excuse me, does your dog bite?" The woman replied, "No, my dog doesn't bite." Hearing this, Jack continued walking. Suddenly the dog jumped up and bit Jack. Jack complained to the woman, "Hey! You said your dog doesn't bite!" The woman said, "It doesn't, but that's not my dog!"
50. What is the best title for this story? (A) A Big Misunderstanding (B) Friends (C) Happy Time (D) Birthday Party
49. Did the woman tell a lie? (A) No, he didn't. (B) No, she didn't. (C) Yes, she did. (D) Yes, he did.
48. Why did Jack stop when he saw the big dog? (A) Because the dog is too big. (B) Because Jack thought it was his dog. (C) Because the dog was running to him. (D) Because the dog was barking at him.