Advertisements
Advertisements
प्रश्न
If f(x) = `{{:((x^3 + x^2 - 16x + 20)/(x - 2)^2",", x ≠ 2),("k"",", x = 2):}` is continuous at x = 2, find the value of k.
उत्तर
Given f(2) = k.
Now, `lim_(x -> 2) "f"(x) = lim_(x -> 2^+) "f"(x)`
= `lim_(x -> 2) (x^3 + x^2 - 16x + 20)/(x - 2)^2`
= `lim_(x -> 2) ((x - 5)(x - 2)^2)/(x - 2)^2`
= `lim_(x -> 2) (x + 5)`
= 7
As f is continuous at x = 2, we have
`lim_(x -> 2) "f"(x)` = f(2)
⇒ k = 7.
APPEARS IN
संबंधित प्रश्न
If \[f\left( x \right) = \begin{cases}\frac{\sin 3x}{x}, when & x \neq 0 \\ 1 , when & x = 0\end{cases}\]
Find whether f(x) is continuous at x = 0.
Discuss the continuity of the function f(x) at the point x = 0, where \[f\left( x \right) = \begin{cases}x, x > 0 \\ 1, x = 0 \\ - x, x < 0\end{cases}\]
Discuss the continuity of the function f(x) at the point x = 1/2, where \[f\left( x \right) = \begin{cases}x, 0 \leq x < \frac{1}{2} \\ \frac{1}{2}, x = \frac{1}{2} \\ 1 - x, \frac{1}{2} < x \leq 1\end{cases}\]
In each of the following, find the value of the constant k so that the given function is continuous at the indicated point;
Prove that \[f\left( x \right) = \begin{cases}\frac{x - \left| x \right|}{x}, & x \neq 0 \\ 2 , & x = 0\end{cases}\] is discontinuous at x = 0
Find all point of discontinuity of the function
The value of b for which the function
The function \[f\left( x \right) = \frac{x^3 + x^2 - 16x + 20}{x - 2}\] is not defined for x = 2. In order to make f (x) continuous at x = 2, Here f (2) should be defined as
Write an example of a function which is everywhere continuous but fails to differentiable exactly at five points.
Give an example of a function which is continuos but not differentiable at at a point.
If f (x) is differentiable at x = c, then write the value of
Let \[f\left( x \right) = \left( x + \left| x \right| \right) \left| x \right|\]
The function f (x) = sin−1 (cos x) is
If \[f\left( x \right) = \left| \log_e |x| \right|\]
If \[f\left( x \right) = \begin{cases}\frac{1}{1 + e^{1/x}} & , x \neq 0 \\ 0 & , x = 0\end{cases}\] then f (x) is
Examine the continuity of f(x)=`x^2-x+9 "for" x<=3`
=`4x+3 "for" x>3, "at" x=3`
Discuss continuity of f(x) =`(x^3-64)/(sqrt(x^2+9)-5)` For x ≠ 4
= 10 for x = 4 at x = 4
Discuss the continuity of f at x = 1 ,
Where f(x) = `(3 - sqrt(2x + 7))/(x - 1)` for x = ≠ 1
= `(-1)/3` for x = 1
Find the points of discontinuity , if any for the function : f(x) = `(x^2 - 9)/(sinx - 9)`
The total cost C for producing x units is Rs (x2 + 60x + 50) and the price is Rs (180 - x) per unit. For how many units the profit is maximum.
If f(x) = `(e^(2x) - 1)/(ax)` . for x < 0 , a ≠ 0
= 1. for x = 0
= `(log(1 + 7x))/(bx)`. for x > 0 , b ≠ 0
is continuous at x = 0 . then find a and b
If y = ( sin x )x , Find `dy/dx`
The probability distribution function of continuous random variable X is given by
f( x ) = `x/4`, 0 < x < 2
= 0, Otherwise
Find P( x ≤ 1)
Find the value of the constant k so that the function f defined below is continuous at x = 0, where f(x) = `{{:((1 - cos4x)/(8x^2)",", x ≠ 0),("k"",", x = 0):}`
Find the values of p and q so that f(x) = `{{:(x^2 + 3x + "p"",", "if" x ≤ 1),("q"x + 2",", "if" x > 1):}` is differentiable at x = 1
An example of a function which is continuous everywhere but fails to be differentiable exactly at two points is ______.
The composition of two continuous function is a continuous function.
