Advertisements
Advertisements
प्रश्न
If f (x) = | x − a | ϕ (x), where ϕ (x) is continuous function, then
पर्याय
f' (a+) = ϕ (a)
f' (a−) = −ϕ (a)
f' (a+) = f' (a−)
none of these
उत्तर
\[f'\left( a^- \right) = - \phi\left( a \right)\]
Here,
Also,
APPEARS IN
संबंधित प्रश्न
If 'f' is continuous at x = 0, then find f(0).
`f(x)=(15^x-3^x-5^x+1)/(xtanx) , x!=0`
Determine the value of 'k' for which the following function is continuous at x = 3
`f(x) = {(((x + 3)^2 - 36)/(x - 3), x != 3), (k, x = 3):}`
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 following functions at the indicated point(s): (iv) \[f\left( x \right) = \left\{ \begin{array}{l}\frac{e^x - 1}{\log(1 + 2x)}, if & x \neq a \\ 7 , if & x = 0\end{array}at x = 0 \right.\]
If \[f\left( x \right) = \begin{cases}\frac{1 - \cos kx}{x \sin x}, & x \neq 0 \\ \frac{1}{2} , & x = 0\end{cases}\text{is continuous at x} = 0, \text{ find } k .\]
In each of the following, find the value of the constant k so that the given function is continuous at the indicated point;
In each of the following, find the value of the constant k so that the given function is continuous at the indicated point;
In each of the following, find the value of the constant k so that the given function is continuous at the indicated point; \[f\left( x \right) = \begin{cases}kx + 1, if & x \leq 5 \\ 3x - 5, if & x > 5\end{cases}\] at x = 5
Let\[f\left( x \right) = \left\{ \begin{array}\frac{1 - \sin^3 x}{3 \cos^2 x} , & \text{ if } x < \frac{\pi}{2} \\ a , & \text{ if } x = \frac{\pi}{2} \\ \frac{b(1 - \sin x)}{(\pi - 2x )^2}, & \text{ if } x > \frac{\pi}{2}\end{array} . \right.\] ]If f(x) is continuous at x = \[\frac{\pi}{2}\] , find a and b.
Find all the points of discontinuity of f defined by f (x) = | x |− | x + 1 |.
Determine if \[f\left( x \right) = \begin{cases}x^2 \sin\frac{1}{x} , & x \neq 0 \\ 0 , & x = 0\end{cases}\] is a continuous function?
The function
The value of b for which the function
If \[f\left( x \right) = \left\{ \begin{array}a x^2 + b , & 0 \leq x < 1 \\ 4 , & x = 1 \\ x + 3 , & 1 < x \leq 2\end{array}, \right.\] then the value of (a, b) for which f (x) cannot be continuous at x = 1, is
If \[f\left( x \right) = \begin{cases}\frac{1 - \sin^2 x}{3 \cos^2 x} , & x < \frac{\pi}{2} \\ a , & x = \frac{\pi}{2} \\ \frac{b\left( 1 - \sin x \right)}{\left( \pi - 2x \right)^2}, & x > \frac{\pi}{2}\end{cases}\]. Then, f (x) is continuous at \[x = \frac{\pi}{2}\], if
Show that f(x) = x1/3 is not differentiable at x = 0.
Show that the function f defined as follows, is continuous at x = 2, but not differentiable thereat:
Write the points of non-differentiability of
The function f (x) = e−|x| is
If \[f\left( x \right) = \left| \log_e x \right|, \text { then}\]
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 the function f at x = 0
If f(x) = `(2^(3x) - 1)/tanx`, for x ≠ 0
= 1, for x = 0
Find the points of discontinuity , if any for the function : f(x) = `(x^2 - 9)/(sinx - 9)`
If the function f is continuous at x = 0
Where f(x) = 2`sqrt(x^3 + 1)` + a, for x < 0,
= `x^3 + a + b, for x > 0
and f (1) = 2, then find a and b.
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
Find the value of 'k' if the function
f(x) = `(tan 7x)/(2x)`, for x ≠ 0.
= k for x = 0.
is continuous at x = 0.
Examine the continuity of the followin function :
`{:(,f(x),=x^2cos(1/x),",","for "x!=0),(,,=0,",","for "x=0):}}" at "x=0`
Show that the function f defined by f(x) = `{{:(x sin 1/x",", x ≠ 0),(0",", x = 0):}` is continuous at x = 0.
The number of points at which the function f(x) = `1/(x - [x])` is not continuous is ______.
The function given by f (x) = tanx is discontinuous on the set ______.
Examine the continuity of the function f(x) = x3 + 2x2 – 1 at x = 1
f(x) = `{{:(|x|cos 1/x",", "if" x ≠ 0),(0",", "if" x = 0):}` at x = 0
Given the function f(x) = `1/(x + 2)`. Find the points of discontinuity of the composite function y = f(f(x))
Examine the differentiability of f, where f is defined by
f(x) = `{{:(x^2 sin 1/x",", "if" x ≠ 0),(0",", "if" x = 0):}` at x = 0
A function f: R → R satisfies the equation f( x + y) = f(x) f(y) for all x, y ∈ R, f(x) ≠ 0. Suppose that the function is differentiable at x = 0 and f′(0) = 2. Prove that f′(x) = 2f(x).
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
The value of k (k < 0) for which the function f defined as
f(x) = `{((1-cos"kx")/("x"sin"x")"," "x" ≠ 0),(1/2"," "x" = 0):}`
is continuous at x = 0 is:
If the following function is continuous at x = 2 then the value of k will be ______.
f(x) = `{{:(2x + 1",", if x < 2),( k",", if x = 2),(3x - 1",", if x > 2):}`