Continuity and Differentiability

Which one of the following is not true?

• Every polynomial function is continuous

• Every rational function is continuous

• Every differential function is continuous

• Every continuous function is differentiable

• 15e
• 5e
• 20e
• 10e

The derivative of log ( cosec x - cot x) with respect to x is

• cot x

• cosec x

• cosec x cot x

• cosec x + cot x

The second order derivative of log x with respect to x is

• 0

• Statement 1 is true and Statement 2 is false

• Statement 1 is true and Statement 2 is true, Statement 2 is correct explanation for statement 1

• Statement 1 is true and Statement 2 is true, Statement 2 is not correct explanation for statement 1

• Statement 1 is false and Statement 2 is false

• Statement 1 is false, and Statement 2 is true.
• Statement 1 is false, and Statement 2 is true

• Statement 1 is true, and Statement 2 is true, Statement 2 is the correct explanation for Statement 1

• Statement 1 is true, and Statement 2 is true, Statement 2 is the not correct explanation for Statement 1

Number of points of discontinuity of a function f(x) = [x] in the interval (-1, 2) where [x] represent greatest integer function less than or equal to x

• 4
• 2
• 1
• 3

• none of these

• 3
• -2
• 0
• -3