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Let x ≠ 0. Find the value of f at x = 0 so that f becomes continuous at x = 0.
For f(x) to be continuous at x = 0, f(0)–= f(0) + =f(0)
LHL = f(0)– =
hence,f(0) =
Test the continuity of the following function at the origin :
A function f(x) is defined as Show that f(x) is continuous at x = 3.
A function f(x) is defined as
Show that f(x) is continuous at x = 3.
If Find whether f(x) is continuous at x = 1.
If Find whether f(x) is continuous at x = 0.
If Find whether f is continuous at x = 0.
Let Show that f(x) is discontinuous at x = 0.
Show that is discontinuous at x = 0.
Show that is discontinuous at x = a.
Discuss the continuity of the following functions at the indicated point(s).
at x = 0
atx = a
at x = 1
at x = a
Show that is discontinuous at x = 1.
Show that is continuous at x = 0
Find the value of ‘a’ for which the function f defined by is continuous at x = 0.
Examine the continuity of the function at x = 0. Also sketch the graph of this function.
Discuss the continuity of the function at the point x = 0.
Discuss the continuity of the function at the point x = 1/2.
Discuss the continuity of at x = 0.
For what value of k is the function continuous atx = 1?
Determine the value of the constant k so that the function is continuous at x = 1.
For what value of k is the function continuous atx = 0?
Determine the value of the constant k so that the function is continuous at x = 2.
Determine the value of the constant k so that the function is continuous at x = 0.
Find the values of a so that the function is continuous at x = 2.
Prove that the function remains discontinuous at x = 0, regardless of the choice of k.
Find the value of k if f(x) is continuous at x = π/2, where
Determine the values of a, b, c for which the function is continuous at x = 0.
If is continuous at x = 0, find k.
If is continuous at x = 4, find a, b.
For what value of k is the function continuous at x = 0?
If is continuous at x = 2, find k.
Extend the definition of the following by continuity at the point x = π.
If is continuous at x = 0, then find f(0).
Find the value of k for which is continuous at x = 0.
In each of the following, find the value of the constant k so that the given function is continuous at the indicated point :
at x = 5
at x = 2.
Find the values of a and b so that the function f given by is continuous at x = 3 and x = 5
If Show that f is continuous at x = 1.
Discuss the continuity of the f(x) at the indicated points :
f(x) = |x| + |x – 1| at x = 0, 1.
f(x) = |x – 1| + |x + 1| at x = – 1, 1.
Prove that is discontinuous at
x = 0.
If then what should be the value of k so that f(x) is continuous at x = 0.
For what value of is the function continuous at x = 0? What about continuity at x = ± 1?
For what value of k is the following function continuous at x = 2?
Let . If f(x) is continuous at find a and b.
If the function f(x), defined below is continuous at x = 0, find the value of k:
Find the relationship between ‘a’ and ‘b’ so that the function ‘f’ defined by is continuous at x = 3.