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intdx=x+c...

`intdx=x+c`

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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

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.)