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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A: The solution is given below in the next step:

Q: True or false: There exists a monotonic function f: R → R whose range is the set of integers. True…

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Q: If f is a function from [-2,6] to R, and f(x) = 3x, partition p = {-2,3,4, 6} and tags e = {0, 4,…

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Q: Let 1 f(x) 2 f(=) = ;= - 7, - 4 < x < 10 -1 The domain of f is the interval [A, B] where A Preview…

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Q: 15-18. Find the extrema of f(x) = 3x - 4x³ on the interval [0, 2].

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A: As per our guidelines, we can answer only three sub-parts in a single request. Kindly re-post the…

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Q: 4 True or False. Explain briefly (you can use diagram to show, or one or two short sentences). (a)…

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A: The given function is: f(x)=2x3-3x2+10 Now, f'(x)=2(3x2)-3(2x)=6x2-6x=6x(x-1)

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Q: Let f be the function defined by f (x) = 6x. On which open intervals is ƒ decreasing? %3D -2 3 <글…

A: Given that: f(x)=x33-x22-6x

Q: 1. F(x) ; (3, 7), [-6, 4], (-co, 0), (-5, +∞), [-5, +∞), [10, -5) %3D x+5 2. F(x) =: (0, 1), (-1,…

A: To find the domain of the function.

Q: A continuous real-valued function f (x) with f (a) ƒ (b) < 0 , has at least one root in [a, b]

A: This question is related to Real Analysis.

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.