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Solved Examples
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 DDD If f(x) = 1x2+9, then which of the following statement(s) is/are correct?I. f(x) is continuous on the interval [- 1, 3]II. f(x) is not right continuous at - 1III. f(x) is continuous on the interval [- 4, 0]IV. f(x) is not left continuous at 0 DDD View Solution
 DDD Which of the following statements are correct for the function f(x) = x2 - 3x - 10 using the Intermediate Value Theorem?I. f(x) has a zero on [- 3, - 1]II. f(x) has no zero on [4, 6]III. f(x) has no zero on [-1, 0]IV. f(x) has no zero on [- 3, - 1] DDD View Solution
 DDD Use Intermediate Value Theorem to choose the correct statement from the following for the function f(x) = 4x2+3xx-1.I. f(x) has a zero on [- 12, 12]II. f(x) has no zero on [- 2, -1]III. f(x) has a zero on [2, 3]IV. f(x) has a zero on [3, 4] DDD View Solution
 DDD Use Intermediate Value Theorem to choose the correct statements from the following for the function f(x) = e2x - 2x.I. f(x) has a zero on [- 2, - 1]II. f(x) has a zero on [0, 12]III. f(x) has no zero on [12, 1]IV. f(x) has no zero on [- 1, 0] DDD View Solution
 DDD Use Intermediate Value Theorem to choose the correct statements for the function f(x) = sin x. DDD View Solution
 DDD Use Intermediate Value Theorem to choose the correct statements from the following for the function f(x) = - x + ln(x2 + 1).I. f(x) has a zero on [- 1, 1]II. f(x) has no zero on [1, 2]III. f(x) has a zero on [- 2, - 1]Iv. f(x) has a zero on [2, 3] DDD View Solution
 DDD Use Intermediate Value Theorem to choose the correct statements from the following for the function f(x) = 2x - 25-x2.I. f(x) has a zero on [2, 3]II. f(x) has no zero on [1, 2]III. f(x) has a zero on [3, 4]IV. f(x) has a zero on [- 3, - 2]  cc View Solution
 cc  Use Intermediate Value Theorem to choose the correct statements from the following for the function f(x) = | 2x + 3 |.I. f(x) has a zero on [1, 2]II. f(x) has no zero on [- 3, - 2]III. f(x) has no zero on [- 2, - 1]IV. f(x) has a zero on [-1, 0]  cc View Solution
 cc  Use Intermediate Value Theorem to choose the correct statements from the following for the function f(x) = 2xx2+4.I. f(x) has a zero on [- 1, 1]II. f(x) has no zero on [- 2, - 1]III. f(x) has a zero on [1, 2]IV. f(x) has a zero on [- 3, - 2]  cc View Solution
 cc  Use Intermediate Value Theorem to choose the correct statements for the function f(x) = sin 2x + cos 2x.  cc View Solution
 cc  By using Intermediate Value Theorem, choose the correct statements from the following for the function f(x) = 2xx2+5.I. f(x) has a zero on [- 12, 12]II. f(x) has a zero on [12, 1]III. f(x) has a zero on [1, 2]IV. f(x) has no zero on [- 2, - 12]  cc View Solution
 cc  Which of the following statement(s) is/are correct for the function f(x) = cos x?I. f(x) is continuous on the interval [0, 4π]II. f(x) is continuous on the interval [ - 4π, - π2]III. f(x) is not right continuous at 0IV. f(x) is not left continuous at - π2  cc View Solution
 cc  If f(x) = x(x + 2) and g(x) = 9-x2, then which of the following statement(s) is/are correct?I. f(x) is continuous on the interval [- 2, 2]II. g(x) is not right continuos at - 3III. f(x) is not left continuous at - 2IV. g(x) is continuous on the interval [- 3, 3]  cc View Solution
 cc  If f(x) = x2 + 2x + 3 and g(x) = ln (x - 3), then which of the following statement(s) is/are correct?I. f(x) is continuous on the interval [0, 2]II. f(x) is not right continuous at 0III. g(x) is not left continuous at 6IV. g(x) is continuous on the interval (3, 6]  cc View Solution
 cc  Choose the correct statement about the continuity of the function. f(x) = 1(x-1)(x-2).  cc View Solution
 cc  Choose the correct statement about the continuity of the function.f(x) = x2+xx+1, x ≠ - 1 and f(- 1) = - 2  cc View Solution
 cc  If f(x) = ex2+2 and g(x) = x3+2x2-x-2x+2, x ≠ - 2 and g(- 2) = 1 then choose the correct statement(s):I. f(x) is not left continuous at 3II. f(x) is continuous on the interval [0, 3]III. g(x) is continuous on the interval (- 2, 2]IV. g(x) is right continuous at - 2  cc View Solution
 cc  Choose the correct statement about the continuity of the function. g(x) = sin xx, x ≠ 0 and g(0) = 1  cc View Solution
 cc  If f(x) = 2 + x where x ≤ 0            = 2 + 12 x2 where x > 0, then which of the following statement(s) is/are correct?I. f(x) is continuous on the interval [- 1, 4]II. f(x) is not right continuous at - 1III. f(x) is continuous on the interval [- 5, - 3]IV. f(x) is not left continuous at - 3  cc View Solution
 cc  Choose the correct statement about the continuity of the function.f(x) = 1x+1, where x > 0           = x3 + 2, where x ≤ 0  cc View Solution