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Higher Study | Mathematics | Limit and Continuity

Suppose, log3 x = log12 y = a, where x, y are positive numbers. If G is the geometric mean of x and y, and log6 G is equal to
Consider the following statements: 1. f(x) = [x], where [.] is the greatest integer function, is discontinuous at x = n, where n ϵ Z. 2. f(x) = cot x is discontinuous at x = nπ, where n ϵ Z.   Which of the above statements is/are correct?
At how many points is the function f(x) = [x] discontinuous?
Consider the following statements in respect of f(x) = |x| - 1 1. f(x) is continuous at x = 1. 2. f(x) is differentiable at x = 0. Which of the above statements is/are correct?
If p > q >1 and 0 < a < 1 then which of the following is correct option?
Which of the following statements is/are true: 1. sin x is a periodic function with period 2π 2. cos x is a periodic function with period 2π
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