A function f:[0,1] -R satisfies f(0)<0 and f(1)>1, and there exists a function g continuous on [0,1] and such that f+g is decreasing. Prove that the equation f(x)=0 has a solution in the open interval (0,1). 0401200002

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.