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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