true or false questions . but please explain why. important 1- for all functions y=f(x) defined on [0,1], the set (f[0,1]) is a bounded set 2- all functions that are continuous on (0,1] are bounded 3- if y=f(x) is an increasing  function on the interval (a,b), and the set {f(x):a{0,1} and I is an interval on which f has both values, then f has a discontinuity in I . 5- if the limit of a function at x=c is 5 , then f(c)=5 6- the function y=f(x) is defined as follows: f(x)=3+ [sin(x-2)/(x-2)] if x≠2 and f(2)=4. then y=f(x) is continuous at all real numbers x.

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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.