Test of Continuity of Functions

The video tutorial explains the concept of continuity in functions, detailing the conditions required for a function to be continuous at a point and within an interval. It covers the continuity of standard functions like constant, trigonometric, exponential, and logarithmic functions, highlighting their domains. The tutorial also discusses discontinuity, providing examples of when and why a function might be discontinuous.

What is the first condition to check if a function is continuous at a point?

• The function must be differentiable at that point.

• The function must be defined at that point.

• The function must have a maximum at that point.

• The function must be increasing at that point.

Which of the following functions is continuous for all real numbers?

• Logarithmic function

• Constant function

• Tangent function

• Cosecant function

Where is the tangent function not continuous?

• At odd multiples of π/2

• At even multiples of π

• At zero

• At all real numbers

Which trigonometric function is not defined at integral multiples of π?

• Secant function

• Cosecant function

• Cosine function

• Sine function

Exponential functions are continuous over which domain?

• Only integers

• Only negative real numbers

• All real numbers

• Only positive real numbers

Logarithmic functions are continuous over which domain?

• All real numbers

• Only positive real numbers

• Only negative real numbers

• Only integers

What might cause a function to be discontinuous at a point?

• The function is constant at that point.

• The function is increasing at that point.

• The function is not defined at that point.

• The function is differentiable at that point.