If g(x)≤f(x)≤h(x)g(x) \le f(x) \le h(x)g(x)≤f(x)≤h(x) near ccc and limx→cg(x)=limx→ch(x)=L\displaystyle\lim_{x \to c} g(x) = \lim_{x \to c} h(x) = Lx→climg(x)=x→climh(x)=L, then limx→cf(x)=L\displaystyle\lim_{x \to c} f(x) = Lx→climf(x)=L. This handles oscillating functions such as xsin(1x)x \sin\left(\dfrac{1}{x}\right)xsin(x1).
12 questions.