So I'm trying to grasp the epsilon,delta definition of limits.(Well not really,I'm actually just trying to be able to get the majority of the related questions right.) For example: when taking limits of rational functions: A result of 0/0 is indeterminate form(suggesting a hole in the function) integer/0 does not exist(or does the limit go to infinity??) 0/integer is a decreasing function(the limit is 0??) are these good rules of thumb or just a lot of hogwash that I've adopted ? also questions like these: use the intermediate value theorem to show that there is a solution of the given equation on the interval [1,2] 2x^3 - 4x^2 +5x -4 = 0. unfortunately there are several types of questions in my book which I am required to know how to answer,yet the book provides insufficient(in my brain)explanation.(Basically I'm just asking not to flame me coz I cant attempt that question...) A continuity question that I'd like checked because I think there's an error in my books provided answer: State the types of discontinuities present for the piecewise defined function: h(x) 2x+9, when x<2 x^2+1 when -2<x<=1 3x-1, when 1<x<3 x+6, when 3<x My book states that there is a removable discontinuity at x=-2... Your help will be greatly appreciated!!