Advertisements
Advertisements
प्रश्न
If f(x) = `{{:("a"x + 1, "if" x ≥ 1),(x + 2, "if" x < 1):}` is continuous, then a should be equal to ______.
Advertisements
उत्तर
If f(x) = `{{:("a"x + 1, "if" x ≥ 1),(x + 2, "if" x < 1):}` is continuous, then a should be equal to a = 2.
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
Find the values of p and q for which
f(x) = `{((1-sin^3x)/(3cos^2x),`
is continuous at x = π/2.
Prove that the function f(x) = 5x – 3 is continuous at x = 0, at x = –3 and at x = 5.
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) = `{(2x + 3", if" x<=2),(2x - 3", if" x > 2):}`
Find all points of discontinuity of f, where f is defined by:
f(x) = `{(|x|/x", if" x != 0),(0", if" x = 0):}`
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):}`
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|.
Using mathematical induction prove that `d/(dx) (x^n) = nx^(n -1)` for all positive integers n.
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
Test the continuity of the function on f(x) at the origin:
\[f\left( x \right) = \begin{cases}\frac{x}{\left| x \right|}, & x \neq 0 \\ 1 , & x = 0\end{cases}\]
Find the points of discontinuity, if any, of the following functions:
Find the points of discontinuity, if any, of the following functions: \[f\left( x \right) = \begin{cases}2x , & \text{ if } & x < 0 \\ 0 , & \text{ if } & 0 \leq x \leq 1 \\ 4x , & \text{ if } & x > 1\end{cases}\]
Find the points of discontinuity, if any, of the following functions: \[f\left( x \right) = \begin{cases}- 2 , & \text{ if }& x \leq - 1 \\ 2x , & \text{ if } & - 1 < x < 1 \\ 2 , & \text{ if } & x \geq 1\end{cases}\]
Discuss the Continuity of the F(X) at the Indicated Points : F(X) = | X − 1 | + | X + 1 | at X = −1, 1.
Find the point of discontinuity, if any, of the following function: \[f\left( x \right) = \begin{cases}\sin x - \cos x , & \text{ if } x \neq 0 \\ - 1 , & \text{ if } x = 0\end{cases}\]
Prove that `1/2 "cos"^(-1) ((1-"x")/(1+"x")) = "tan"^-1 sqrt"x"`
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.
`lim_("x" -> pi/2)` [sinx] is equal to ____________.
The number of discontinuous functions y(x) on [-2, 2] satisfying x2 + y2 = 4 is ____________.
If f(x) `= sqrt(4 + "x" - 2)/"x", "x" ne 0` be continuous at x = 0, then f(0) = ____________.
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^10 - 1",", if x ≤ 1),(x^2",", if x > 1):}` is discontinuous at
Sin |x| is a continuous function for
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 ______.
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.
The graph of the function f is shown below.
Of the following options, at what values of x is the function f NOT differentiable?
