(1) The parts in this question are not related to each other. 4 1 (a) ) Using the e – ổ definition of limit, prove that lim 1+3 3r – 1 (b) Let f : R →R be a function with the following property: \f(a) – f(b)| < 4|a – b| for all a, b e R. Prove that f is continuous everywhere. (c) Show that the function g(x) = r³ – 7x² + 25x + 8 has exactly one real root.
(1) The parts in this question are not related to each other. 4 1 (a) ) Using the e – ổ definition of limit, prove that lim 1+3 3r – 1 (b) Let f : R →R be a function with the following property: \f(a) – f(b)| < 4|a – b| for all a, b e R. Prove that f is continuous everywhere. (c) Show that the function g(x) = r³ – 7x² + 25x + 8 has exactly one real root.
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Transcribed Image Text:(1) The parts in this question are not related to each other.
4
Using the e - ô definition of limit, prove that lim
1
(a)
I+3 3x - 1
(b) (
Let f : R → R be a function with the following property:
|f(a) – f(b)| < 4|a – b| for all a, b E R.
Prove that f is continuous everywhere.
(c)
Show that the function g(x) = x³ – 7x² + 25x + 8 has exactly one real root.
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