# DETERMINE IF A FUNCTION IS CONTINUOUS AT A POINT WORKSHEET

Problem 1 :

continuous at x = -1 and continuous at x = 2 ?

Solution

Problem 2 :

continuous at x = 1 ?

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

The function f has the properties indicated in the table below. Which of the following must be true ?

a)  f is continuous at x = 1        b)  f is continuous at x = 2

c)  f is continuous at x = 3        d)  None of the above.

Solution

Problem 6 :

If the function f is continuous for all real numbers and if

f(x) = (x2 - 4)/(x + 2)

when x ≠ 2, then f(-2) =

A) -4   B)  -2   C)  -1  D) 0   E) 2

Solution

Problem 7 :

Let f be the function given above. What are all values of a and b for which f is differentiable at x = 2 ?

a) 1/4 and b = -1/2

b)  a = 1/4 and b = 1/2

c)  a = 1/4 and b is any real number]

d)  a = b + 2 where b is any real number

e)  There are no such values of a and b.

Solution

## Answer Key

1)  The function is continuous at x = -1.

The function is not continuous at x = 2.

2)  So, the function g(x) is not continuous at x = 1.

3) The function is not continuous at x = -3 and continuous at x = 4.

4)  So, the function f(x) is not continuous at x=π/2 and continuous at x = π.

5)  lim x->3- f(x) and lim x->3+ f(x) they are equal. So, the function f(x) is continuous at x --> 3, option c.

6)  So, the answer is -4.

7)  So, option a is correct.

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