Question

1. Determine whether the statement is true or false. If false, explain why and correct the statement (T/FIf)exists, then lim ()f) o( T / F ) If f is continuous, then lim f(x) = f(r) (TFo)-L, then lim f(x)- lim F(x) "( T / F ) If lim -f(x)s lim. f(x) L, then lim f(x)s 1. "(T/F) lim. In x -oo . (T/F) lim0 ·(T / F ) The derivative f' (a) is the instantaneous rate of change of y = f(x) with respect to x when x = a. (T/F) If f(x) >0 on an interval, then fis decreasing on that interval (T/F) If ye then y' 2e * ( T / F ) Iff and g are differentiable, then d [f(x)-g(x)--(f(x)) 릎(g(x). * ( T F ) lff and g are differentiable, then d [f(g(x))] = f' (g(x)) + g'(x) (T/F) If f is differentiable at a, then f is continuous at a. dx dx (T/F)If f'(c)0, then f has a local maximum or minimum at c (T/F) If f has an absolute maximum or minimum at c, then f'(c) 0 (T/F) If f is a differentiable function and has a local maximum or minimum at c, then f'(c)0 . ( T/ F ) lff and g are continuous on [a, b], then bh@ .g(x)] dx = (1ケ(x) d9(1 g(x) dx) . ( T / F ) If f is continuous on [a, b], then玿f(x) dx-鉛f(x) dx (T/F) All continuous functions have derivatives. (T F) All continuous functions have antiderivatives

Answer 1

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