Advertisements
Advertisements
प्रश्न
The function f(x) = cot x is discontinuous on the set ______.
पर्याय
{x = nπ : n ∈ Z}
{x = 2nπ : n ∈ Z}
`{x = (2"n" + 1)pi/2 ; "n" ∈ "Z"}`
`{x = ("n"pi)/2 ; "n" ∈ "Z"}`
उत्तर
The function f(x) = cot x is discontinuous on the set {x = nπ : n ∈ Z}.
Explanation:
Given that: f(x) = cot x
⇒ f(x) = `cosx/sinx`
We know that sin x = 0 if f(x) is discontinuous.
∴ If sin x = 0
∴ x = nπ, n ∈ nπ.
So, the given function f(x) is discontinuous on the set {x = nπ : n ∈ Z}.
APPEARS IN
संबंधित प्रश्न
If `sec((x+y)/(x-y))=a^2. " then " (d^2y)/dx^2=........`
(a) y
(b) x
(c) y/x
(d) 0
If `y=sin^-1(3x)+sec^-1(1/(3x)), ` find dy/dx
Find : ` d/dx cos^−1 ((x−x^(−1))/(x+x^(−1)))`
Find the derivative of the following function f(x) w.r.t. x, at x = 1 :
`f(x)=cos^-1[sin sqrt((1+x)/2)]+x^x`
if `y = sin^(-1)[(6x-4sqrt(1-4x^2))/5]` Find `dy/dx `.
If `y=tan^(−1) ((sqrt(1+x^2)+sqrt(1−x^2))/(sqrt(1+x^2)−sqrt(1−x^2)))` , x2≤1, then find dy/dx.
Find `dx/dy` in the following:
`y = cos^(-1) ((2x)/(1+x^2)), -1 < x < 1`
Find `dy/dx` in the following:
`y = sin^(-1)(2xsqrt(1-x^2)), -1/sqrt2 < x < 1/sqrt2`
Differentiate w.r.t. x the function:
`cot^(-1) [(sqrt(1+sinx) + sqrt(1-sinx))/(sqrt(1+sinx) - sqrt(1-sinx))]`, ` 0 < x < pi/2`
Find `dy/dx, if y = sin^-1 x + sin^-1 sqrt (1 - x^2) , 0<x <1`
Find the approximate value of tan−1 (1.001).
Differentiate `tan^(-1) ((1+cosx)/(sin x))` with respect to x
Solve `cos^(-1)(sin cos^(-1)x) = pi/2`
If y = (sec-1 x )2 , x > 0, show that
`x^2 (x^2 - 1) (d^2 y)/(dx^2) + (2x^3 - x ) dy/dx -2 = 0`
If y = cos (sin x), show that: `("d"^2"y")/("dx"^2) + "tan x" "dy"/"dx" + "y" "cos"^2"x" = 0`
If y = sin-1 x + cos-1x find `(dy)/(dx)`.
If y = `(sin^-1 x)^2,` prove that `(1-x^2) (d^2y)/dx^2 - x dy/dx -2 = 0.`
`lim_("h" -> 0) (1/("h"^2 sqrt(8 + "h")) - 1/(2"h"))` is equal to ____________.
`lim_("x" -> -3) sqrt("x"^2 + 7 - 4)/("x" + 3)` is equal to ____________.
If y `= "cos"^2 ((3"x")/2) - "sin"^2 ((3"x")/2), "then" ("d"^2"y")/("dx"^2)` is ____________.
The derivative of sin x with respect to log x is ____________.
If y = sin–1x, then (1 – x2)y2 is equal to ______.
Differentiate `sec^-1 (1/sqrt(1 - x^2))` w.r.t. `sin^-1 (2xsqrt(1 - x^2))`.
