Advertisements
Advertisements
प्रश्न
The function f (x) = tan x is discontinuous on the set
विकल्प
{n π : n ∈ Z}
{2n π : n ∈ Z}
\[\left\{ \left( 2n + 1 \right)\frac{\pi}{2}: n \in Z \right\}\]
\[\left\{ \frac{n\pi}{2}: n \in Z \right\}\]
Advertisements
उत्तर
When
Hence,
APPEARS IN
संबंधित प्रश्न
Discuss the continuity of the following functions. If the function have a removable discontinuity, redefine the function so as to remove the discontinuity
`f(x)=(4^x-e^x)/(6^x-1)` for x ≠ 0
`=log(2/3) ` for x=0
Show that the function `f(x)=|x-3|,x in R` is continuous but not differentiable at x = 3.
Find the values of p and q for which
f(x) = `{((1-sin^3x)/(3cos^2x),`
is continuous at x = π/2.
Examine the continuity of the function f(x) = 2x2 – 1 at x = 3.
Find all points of discontinuity of f, where f is defined by:
f(x) = `{(x/|x|", if" x<0),(-1", if" x >= 0):}`
Find all points of discontinuity of f, where f is defined by:
f(x) = `{(x^10 - 1", if" x<=1),(x^2", if" x > 1):}`
Is the function defined by f(x) = `{(x+5", if" x <= 1),(x -5", if" x > 1):}` a continuous function?
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.
Examine the continuity of f, where f is defined by:
f(x) = `{(sin x - cos x", if" x != 0),(-1", if" x = 0):}`
Find all the points of discontinuity of f defined by f(x) = |x| − |x + 1|.
Determine the value of the constant 'k' so that function f(x) `{((kx)/|x|, ","if x < 0),(3"," , if x >= 0):}` is continuous at x = 0
Find the value of constant ‘k’ so that the function f (x) defined as
f(x) = `{((x^2 -2x-3)/(x+1), x != -1),(k, x != -1):}`
is continous at x = -1
Show that the function f(x) = `{(x^2, x<=1),(1/2, x>1):}` is continuous at x = 1 but not differentiable.
Find the points of discontinuity, if any, of the following functions:
In the following, determine the value of constant involved in the definition so that the given function is continuou:
Discuss the Continuity of the F(X) at the Indicated Points : F(X) = | X − 1 | + | X + 1 | at X = −1, 1.
Show that the function f given by:
`f(x)={((e^(1/x)-1)/(e^(1/x)+1),"if",x,!=,0),(-1,"if",x,=,0):}"`
is discontinuous at x = 0.
Find all points of discontinuity of the function f(t) = `1/("t"^2 + "t" - 2)`, where t = `1/(x - 1)`
`lim_("x" -> pi/2)` [sinx] is equal to ____________.
Let f (x) `= (1 - "tan x")/(4"x" - pi), "x" ne pi/4, "x" in (0, pi/2).` If f(x) is continuous in `(0, pi/2), "then f"(pi/4) =` ____________.
If f(x) `= sqrt(4 + "x" - 2)/"x", "x" ne 0` be continuous at x = 0, then f(0) = ____________.
`lim_("x"-> 0) sqrt(1/2 (1 - "cos" 2"x"))/"x"` is equal to
The function f defined by `f(x) = {{:(x, "if" x ≤ 1),(5, "if" x > 1):}` discontinuous at x equal to
How many point of discontinuity for the following function in its. domain.
`f(x) = {{:(x/|x|",", if x < 0),(-1",", if x ≥ 0):}`
`f(x) = {{:(x^3 - 3",", if x < 2),(x^2 + 1",", if x > 2):}` has how many point of discontinuity
Sin |x| is a continuous function for
If function f(x) = `{{:((asinx + btanx - 3x)/x^3,",", x ≠ 0),(0,",", x = 0):}` is continuous at x = 0 then (a2 + b2) is equal to ______.
If functions g and h are defined as
g(x) = `{{:(x^2 + 1, x∈Q),(px^2, x\cancel(∈)Q):}`
and h(x) = `{{:(px, x∈Q),(2x + q, x\cancel(∈)Q):}`
If (g + h)(x) is continuous at x = 1 and x = 3, then 3p + q is ______.
If f(x) = `{{:(cos ((π(sqrt(1 + x) - 1))/x)/x,",", x ≠ 0),(π/k,",", x = 0):}`
is continuous at x = 0, then k2 is equal to ______.
If f(x) = `{{:((log_(sin|x|) cos^2x)/(log_(sin|3x|) cos x/2), |x| < π/3; x ≠ 0),(k, x = 0):}`, then value of k for which f(x) is continuous at x = 0 is ______.
Let α ∈ R be such that the function
f(x) = `{{:((cos^-1(1 - {x}^2)sin^-1(1 - {x}))/({x} - {x}^3)",", x ≠ 0),(α",", x = 0):}`
is continuous at x = 0, where {x} = x – [x], [x] is the greatest integer less than or equal to x.
If the function f defined as f(x) = `1/x - (k - 1)/(e^(2x) - 1)` x ≠ 0, is continuous at x = 0, then the ordered pair (k, f(0)) is equal to ______.
Find the value(s) of 'λ' if the function
f(x) = `{{:((sin^2 λx)/x^2",", if x ≠ 0 "is continuous at" x = 0.),(1",", if x = 0):}`
