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

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

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

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