math151au09es.border.17.Hmwk2

# math151au09es.border.17.Hmwk2 - Andrew Robert Border...

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Andrew Robert Border - Homework 2 due Fri, Oct 9 at 11:59 pm Course: math151au09es This problem set covers Sections 2.5 - 2.9. Recitation Call#: . Carefully read all instructions for entering answers into WeBWorK. Set: Hmwk2 1. (2 pts) [rgb]0,0.07,0.45 Click on the graph to get an enlarged view. Let the function f ( x ) be given by the depicted graph on the interval [ - 6 , 10 ] . List, in order, the maximal intervals on which f is continu- ous, separated by commas. [rgb]0,0.07,0.45 Include endpoints at which f ( x ) is one-sided continuous on the respective interval by square brackets [rgb]0.6,0,0 ’[’ or [rgb]0.6,0,0 ’]’ , and exclude endpoints by [rgb]0.6,0,0 ’(’ or [rgb]0.6,0,0 ’)’ where f ( x ) is dis- continuous. Indicate the values of x where f ( x ) is discontinuous. Start with the leftmost point. For each of the values state whether f ( x ) is continuous from the right (input R), or from the left (in- put L). at x = f ( x ) is continuous from ; at x = f ( x ) is continuous from ; at x = f ( x ) is continuous from . 2. (2 pts) Use continuity to evaluate lim x 1 e x 4 - x 2 Enter I for , -I for - , and DNE if the limit does not exist. Limit = 3. (2 pts) Let f ( x ) = ± mx - 10 , if x < - 7 x 2 + 9 x - 3 , if x ≥ - 7 If f ( x ) is a function which is continuous everywhere, then we must have m = Now for fun, try to graph f ( x ) . 4. (2 pts) For what value of c is the function deﬁned below continuous on ( - , ) ? f ( x ) = ± x 2 - c 2 , x < 8 , cx + 80 , x 8 . c = 5. (1 pt) Use the Intermediate Value Theorem to check whether the equation x 3 - 3 x - 6 . 9 = 0 has a root in the interval ( 0 , 1 ) . Check

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math151au09es.border.17.Hmwk2 - Andrew Robert Border...

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