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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?

Let x ≠ 0. Find the value of f at x = 0 so that f becomes 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.

Prove that the function is everywhere continuous.

Discuss the continuity of the function .

Find the points of discontinuity, if any, of the following functions :

In the following, determine the value(s) of constant(s) involved in the definition so that the given function is continuous:

The function is continuous on [0, ∞]. Find the most suitable values of a and b.

Find the values of a and b so that the function f(x) defined by

becomes continuous on [0, π].

The function f(x) is defined by If f is continuous on [0, 8], find the values of a and b.

If for find the value which can be assigned to f(x) at x = π/4 so that the function f(x) becomes continuous every where in [0, π/2].

Discuss the continuity of the function

Discuss the continuity of f(x) = sin |x|.

Prove that is everywhere continuous.

Show that the function g(x) = x – [x] is discontinuous at all integral points. Here [x] denotes the greatest integer function.

Discuss the continuity of the following functions :

f(x) = sin x + cos x

f(x) = sin x – cos x

f(x) = sin x cos x

Show that f(x) = cos x^{2} is a continuous function.

Show that f(x) = |cos x| is a continuous function.

Find all the points of discontinuity of f defined by

f(x) = |x| – |x + 1|.

Is a continuous function?

Given the function Find the points of discontinuity of the function f(f(x)).

Find all point of discontinuity of the function where

Mark the correct alternative in the following:

The function

If f(x) = |x – a| ϕ(x), where ϕ(x) is continuous function, then

If f(x) = |log_{10} x|, then at x = 1

If is continuous at x = 0, then k equals

If f(x) defined by then f(x) is continuous for all

If is continuous at x = π/2, then k =

If f(x) = (x + 1)^{cotx} be continuous at x = 0, then f(0) is equal to

If and f(x) is continuous at x = 0, then the value of k is

Let Then f(x) is continuous at x = 4 when

If the function is continuous at x = 0, then the value of k is

Let f(x) = |x| + |x – 1|, then

Let Then, f(x) is continuous on the set

If is continuous at x = 0, then

If is continuous at then

The value of f(0), so that the function becomes continuous for all x, given by

The value of f(0), so that the function is continuous, is given by

The value f(0) so that the function is continuous everywhere, is given by

is continuous in the interval [–1, 1], then p is equal to

The function is continuous for 0 ≤ x < ∞, then the most suitable values of a and b are

If when then f(x) will be continuous function at x = π/2, where λ =

The value of a for which the function may be continuous at x = 0 is

The function f(x) = tan x is discontinuous on the set

The function is continuous at x = 0, then k =

If the function is continuous at each point of its domain, then the value of f(0) is

The value of b for which the function is continuous at every point of its domain, is

If then the set of points discontinuity of the function f(f(f(x))) is

Let The value which should be assigned to f(x) at so that it is continuous everywhere is

The function is not defined for x = 2. In order to make f(x) continuous at x = 2, f(2) should be defined as

If is continuous at x = 0, then a equals

If then the value of (a, b) for which f(x) cannot be continuous at x = 1, is

If the function f(x) defined by is continuous at x = 0, then k =

If then the value of a so that f(x) may be continuous at x = 0, is

If f(x) = then the value of the function at x = 0, so that the function is continuous at x = 0, is

The value of k which makes continuous at x = 0, is

The values of the constants a, b, and c for which the function

May be continuous at x = 0, are

The points of discontinuity of the function is (are)

If ..Then, f(x) is continuous at if

The points of discontinuity of the

function is (are)

The value of a for which the function is continuous at every point of its domain, is

If is

Continuous at then k is equal to

Define continuity of a function at a point.

What happens to a function f(x) at x = a, if

Find f (0), so that becomes continuous at x = 0.

If is continuous at x = 0, then write the value of k.

If the function x ≠ 0 is continuous at x = 0, find f(0).

If is continuous at x = 4, find k.

Determine whether is continuous at x = 0 or not.

If is continuous at x = 0, write the value of k.

Write the value of b for which is continuous at x = 1.

Determine the value of constant ‘k’ so that the function is continuous as x = 0.

Find the value of k for which the function is continuous at x = 2.