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Continuity Theorem

 

.   True or False: If g(x) is continuous at x = c and the function f(x) is continuous at g(c), then fog(x) is continuous at x = c.


.   True or False: If two functions f(x) and g(x) are continuous at a real valued function and continuous at a point x = c, then f(x) + g(x) is not continuous at the point x = c.



.   True or False: If a given function f(x) is continuous at a point x = c, then it is differentiable at that point.


                                                               

          True or False: All continuous functions are differentiable functions.

          True or False: If two functions f(x) and g(x) are continuous at a real valued function and continuous at a point x = c, then f(x) - g(x) is not continuous at a point x = c.

.   True or False: If two functions f(x) and g(x) are continuous at a real valued function and continuous at a point x = c, f(x).g(x) is continuous at point x = c.

          True or False: If two functions f(x) and g(x) are continuous at a real valued function and continuous at a point x = c, f(x)/g(x) is continuous at a point x = c, provided g(c) ≠ 0.

   True or False: All differentiable functions are continuous functions.

  True or False: If two functions f(x) and g(x) are continuous at a real valued function and continuous at a point x = c, then f(x) + g(x) is continuous at the point x = c.

.   True or False: If two functions f(x) and g(x) are continuous at a real valued function and continuous at a point x = c, then f(x) - g(x) is continuous at a point x = c.