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Let y = f(x) be defined in [a, b], then ...

Let y = f(x) be defined in [a, b], then
(i) Test of continuity at `x = c, a lt c lt b`
(ii) Test of continuity at x = a
(iii) Test of continuity at x = b
Case I Test of continuity at `x = c, a lt c lt b`
If y = f(x) be defined at x = c and its value f(c) be equal to limit of f(x) as `x rarr c` i.e. f(c) = `lim_(x to c) f(x)`
or `lim_(x to c^(-))f(x) = f(c) = lim_(x to c^(+)) f(x)`
or LHL = f(c) = RHL
then, y = f(x) is continuous at x = c.
Case II Test of continuity at x = a
If RHL = f(a)
Then, f(x) is said to be continuous at the end point x = a
Case III Test of continuity at x = b, if LHL = f(b)
Then, f(x) is continuous at right end x = b.
Number of points of discontinuity of `[2x^(3) - 5]` in [1, 2) is (where [.] denotes the greatest integral function.)

A

14

B

13

C

10

D

None of these

Text Solution

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The correct Answer is:
B
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Let y = f(x) be defined in [a, b], then (i) Test of continuity at x = c, a lt c lt b (ii) Test of continuity at x = a (iii) Test of continuity at x = b Case I Test of continuity at x = c, a lt c lt b If y = f(x) be defined at x = c and its value f(c) be equal to limit of f(x) as x rarr c i.e. f(c) = lim_(x to c) f(x) or lim_(x to c^(-))f(x) = f(c) = lim_(x to c^(+)) f(x) or LHL = f(c) = RHL then, y = f(x) is continuous at x = c. Case II Test of continuity at x = a If RHL = f(a) Then, f(x) is said to be continuous at the end point x = a Case III Test of continuity at x = b, if LHL = f(b) Then, f(x) is continuous at right end x = b. Max ([x],|x|) is discontinuous at

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