> . Is the function defined by , if , if = − > a continuous function? Discuss the continuity of the function f , where f is defined by . , if , if , if .
, if , if , if > . , if , if , ≤− −< > . Find the relationship between a and b so that the function f defined by , if , if ax bx = > is continuous at x = . .
For what value of λ is the function defined by ), if , λ = > continuous at x = ? What about continuity at x = ? . Show that the function defined by g ( x ) = x – [ x ] is discontinuous at all integral points.
Here [ x ] denotes the greatest integer less than or equal to x . . Is the function defined by f ( x ) = x – sin x + continuous at x = π ? .
Discuss the continuity of the following functions: (a) f ( x ) = sin x + cos x (b) f ( x ) = sin x – cos x (c) f ( x ) = sin x . cos x . Discuss the continuity of the cosine, cosecant, secant and cotangent functions. .
Find all points of discontinuity of f , where , if , = + ≥ . Determine if f defined by , if , ≠ = is a continuous function? . Examine the continuity of f , where f is defined by cos , if , ≠ = − Find the values of k so that the function f is continuous at the indicated point in Exercises to .
. cos , if , k π ≠ π − = π at x = π . , if , kx = > at x