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chapter 2 82 - 146 CHAPTER 2 LIMITS AND DERIVATlVES 1 52...

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Unformatted text preview: 146 CHAPTER 2 LIMITS AND DERIVATlVES 1 52. The slope of the tangent to y = m + 1 is w _ (:c+h)+1 _:c+1 . (:I:+h)—1 x—l _ (a:—1)(x+h+1)e(m+1)(:c+h—1) l ————————:l __—_——————— #35 h 11135 h(m—1)(m+h—1) —2h 2 :liirbmx—ixHh—i) : (m—1)2 Soat(2,3)tm:— =fl2 => y—3:—2(m—2) : (2 #1)2 s 2 1 x — => y 2 7290+? At(—1,0)_m: ____ _§ (51—1)? ’ a ‘4 y=-%(w+1) :> y=r%$'%- ’3’-“ ‘ *4 53. |f(:c)| S g(m) <=> *g(a:) 3 flat) 3 g(:n) and lim g(m) = 0 = lim —g(m). Thus, by the Squeeze Theorem, lim flan) : 0. 54. (a) Note that f is an even function since f (as) : f (—m). Now for any integer n, [[n]] + [PM] : n 4 n : 0, and for any real number k which is not an integer, [16]] + [[7,6]] : [[19]] + (— [Hall A 1): #1. So lim flan) exists :caa. (and is equal to —1) for all values of a. (b) f is discontinuous at all integers. ...
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