MATH137（微积分1）关于函数的连续性的练习题.懂英文的数学大神求教.

MATH137（微积分1）关于函数的连续性的练习题.懂英文的数学大神求教.
1 . State the precise mathematical definition of lim f(x) x→−∞= −∞ . Then use your definition
to prove that lim (1 + 2x^3) x→−∞= −∞
2. Let f(x) be continuous on [0,4] with f(0) = f(4). Show that there exists x ∈ [0,2] such that f(x) = f(x + 2). [Hint: Consider g(x) = f(x + 2)−f(x)]