# 255 sketch the graph of a function f that is

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2.5.5 Sketch the graph of a function f that is continuous except for the stated discontinuity: Discontinuous, but continuous from the right, at 2 2.5.7 Sketch the graph of a function f that is continuous except for the stated discontinuity: Removable discontinuity at 3, jump discontinuity at 5 2.5.20 Explain why the function is discontinuous at x = 1. Sketch the graph of the function. f ( x ) = ( x 2 - x x 2 - 1 if x 6 = 1 1 if x = 1 2.5.21 Explain why the function is discontinuous at x = 0. Sketch the graph of the function. f ( x ) = cos x if x < 0 0 if x = 0 1 - x 2 if x > 0 2.5.23 f ( x ) = x 2 - x - 2 x - 2 How would you “remove the disconti- nuity” of f ? In other words, how would you define f (2) in order to make f continuous at 2? 2.5.43 Find the numbers at which f is discontinuous. At which of these numbers is f continuous from the right, from the left, or neither? Sketch the graph of f . f ( x ) = x + 2 if x < 0 e x if 0 x 1 2 - x if x > 1 2.5.45 For what value of the constant c is the function f continu- ous on ( -∞ , )? f ( x ) = ( cx 2 + 2 x if x < 2 x 3 - cx if x 2 2.5.46* Find the values of a and b that make f continuous every- where. f ( x ) = x 2 - 4 x - 2 if x < 2 a if x = 2 5 x - a + b if x > 2 2.5.53 Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. x 4 + x - 3 = 0 , (1 , 2) 2.5.55 Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. e x = 3 - 2 x, (0 , 1) 2.6.5 Sketch the graph of an example of a function f that satisfies all of the given conditions. lim x 0 f ( x ) = -∞ , lim x →-∞ f ( x ) = 5, lim x →∞ f ( x ) = - 5 2.6.7 Sketch the graph of an example of a function f that satisfies all of the given conditions. lim x 2 f ( x ) = -∞ , lim x →∞ f ( x ) = , lim x →-∞ f ( x ) = 0, lim x 0 + f ( x ) = , lim x 0 - f ( x ) = -∞
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2.6.18 Find the limit or show that it does not exist. 2.6.19 Find the limit or show that it does not exist.
lim t →∞ t + t 2 2 t - t 2 2.6.35 Find the limit or show that it does not exist. 2.6.36 Find the limit or show that it does not exist.