# Exam

Exam

1.-Determine the value of a > 0 knowing that f is continuous

 a) a = -3 b) a = 5 c) a = ± 3 d) a = 3

2.- Determine the value of a and b to do continuous the function:

 a) a = 1; b = 3 b) a = 3; b = 1 c) a = 1; b = -3 d) a = -3; b = -1

3.- Determine the value of a and b to do continuous the function

 a) b = -5; a € R b) b = 5; a € R c) a = 3; b = -1 d) None of them

4.- Study the continuity of the function:

 a) f is continuous in R-{2}. In x = 2 f has a jump discontinuity with jump 2 b) f is continuous in R-{2}. In x = 2 f has a removable discontinuity c) f is continuous in R-{2}. In x = 2 f has a jump discontinuity with jump 1 d) f is continuous in R

5.- Study the continuity of the function

 a) f is continuous in R b) f is continuous in R-{5}. In x = 5 f has a removable discontinuity c) f is continuous in R-{5}. In x = 5 f has a jump discontinuity with jump 10 d) f is continuous in R-{5}. In x = 5 f has a jump discontinuity with jump 5

6.- Determine the value of k to do continuous the function

 a) k = 6 b) k = 1 c) k = -1 d) None of them

7.- Let

Which of these sentences is true?

 a) f is continuous in R-{4} b) f doesn't exist in x = 4 c) f is continuous in its domain d) All of them

8.- Study the continuity of the function

 a) f is continuous in R b) f is continuous in R-{0}. In x = 0 f has a removable discontinuity c) f is continuous in R-{0}. In x = 0 f has an essential discontinuity d) f is continuous in R-{0}. In x = 0 f has an infinity jump discontinuity

9.- To demonstrate that a continuous function in an closed interval has at least one absolute maximum and one absolute minimum, we use ...

 a) the Bolzano's Theorem b) the Bolzano-Weirstrass's Theorem c) the intermediate-value Theorem d) the Pythagorean Theorem

10.- If f and g are discontinuous in x = a

 a) f + g can be continuous in x = a b) f - g can be continuous in x = a c) f · g can be continuous in x = a d) All of them are true