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Practice each question, then open the answer or worked solution.
Examine the continuity of the function f (x) = x3 + 2x2 – 1 at x = 1
We know that, y = f(x) will be continuous at x = a if,
Thus, f(x) is continuous at x = 1.
Find which of the functions in Exercises 2 to 10 is continuous or discontinuous at the indicated points:
at x = 2
Checking the continuity of the given function, we have
Thus, f(x) is discontinuous at x = 2.
at x = 0
Checking the right hand and left hand limits of the given function, we have
Therefore, the given function f(x) is discontinuous at x = 0.
at x = 2
Thus, f(x) is continuous at x = 2.
at x = 4
Checking the right hand and left hand limits for the given function, we have
Thus, f(x) is discontinuous at x = 4.
at x = 0
Checking the right hand and left hand limits for the given function, we have
Thus, the given function f(x) is continuous at x = 0.
at x = a
Checking the right hand and left hand limits for the given function, we have
Thus, the given function f(x) is continuous at x = 0.
at x = 0
Checking the right hand and left hand limits for the given function, we have
Thus, f(x) is discontinuous at x = 0.
at x = 1
Checking the right hand and left hand limits for the given function, we have
Thus, the given function f(x) is continuous at x = 1.
f (x) = |x| + |x – 1| at x = 1
Checking the right hand and left hand limits for the given function, we have
Thus, f(x) is continuous at x = 1.
Find the value of k in each of the Exercises 11 to 14 so that the function f is continuous at the indicated point: