Limits_notes_1.4_Day_2_part_2

Limits_notes_1.4_Day_2_part_2 - ejeétige: Determine values...

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Unformatted text preview: ejeétige: Determine values of constants to create a continuous function. Define the function Make the limit exist Check to see that they are equal a Review solving systems of equations " skews-u, V t A anlues of the constant that Fin cause the functions to be H) XI“: l . 31.11. continuous ,, L3 / it h(x)={ax2+bx,if,x—2|<l I 4 X P.” L 2x+3,zfix—2[21 ‘ 8/29/2011 8/29/2011 Objective: Use the Intermediate Value Theorem If f is continuous on [a, b] and k is any number between f(a) and f(b), then there is at least one number 0 in [a, b] such that f(c) = k Rat) 4L L- Existence theorems u 5) “ Guarantee that some c exists We may not always be able to find that "c The Mean Value Theorem is another important existence theorem that we will study later. 8/29/2011 A function is continuous on an open interval (a,b) if it is continuous at each point in the interval. m A function is continuous on the closed interval [a,b] if it is continuous on the open interval (ab) and limflx) = fla) and lim f(x) = f(b) x—->a+ X—W' illéfi‘a'9fi1s - Verify that the NT applies and find the value of if possible. \) f(x)=x2 +x__1 on [0,5] Is f(x) coniinuous‘? \fiQSL {C’L‘T’km’m . “6):” f(a)=f(0)=U"U" 7 ” I f(b)=f(5)= Z‘it/S 477/” IS f(a)<f(0)<f(b)?/ _ I In lives! I L.(l L‘L‘l V f(c)=c2+c—1 11=c2+c—1 Solve to find c ;( ’5)(?(Hf) 8/29/2011 If f(x)is continuous on [a, b] and if f(a) and f(b) are nonzero and have opposite signs, then f(x) has a zero in (a. b) a a . Explain why f(x) has a zero in the interval (a, b) J f(a)=f(l)= in |--3 : a f(b)=f(2)= fag/3: negative < c < p_0sitive 1% c is zero somewhere in (1, 2) V6 Is f (x) continuous? 21 ) ...
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Limits_notes_1.4_Day_2_part_2 - ejeétige: Determine values...

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