10810 MATH 101007
Calculus I
Exercise 1
2019/10/07
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limf (x) = L.
(A) Let f : R → R be an odd function. Suppose that c > 0 and x→c
lim f (x) = −L.
Show that x→−c
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(B) Let n be an odd positive integer and f (x) = x n , x ∈ R.
(i) Show that f is continuous at c = 0.
lim x n1 = c n1 .
(ii) For any c > 0, show that x→c
lim x n1 = (−c) n1 , for any c > 0.
(iii) Show that x→−c
(
)
Hint: Using the result given in Exercise (A).
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Exercise (B) claims that the function f (x) = x n (n ∈ N, n odd), is continuous on R.
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