Advertisements
Advertisements
प्रश्न
Define differentiability of a function at a point.
Advertisements
उत्तर
Let
APPEARS IN
संबंधित प्रश्न
Find the value of 'k' if the function
`f(X)=(tan7x)/(2x) , "for " x != 0 `
`=k`, for x=0
is continuos at x=0
Let \[f\left( x \right) = \begin{cases}\frac{1 - \cos x}{x^2}, when & x \neq 0 \\ 1 , when & x = 0\end{cases}\] Show that f(x) is discontinuous at x = 0.
Discuss the continuity of the following functions at the indicated point(s):
Discuss the continuity of the following functions at the indicated point(s):
Show that
\[f\left( x \right) = \begin{cases}\frac{\sin 3x}{\tan 2x} , if x < 0 \\ \frac{3}{2} , if x = 0 \\ \frac{\log(1 + 3x)}{e^{2x} - 1} , if x > 0\end{cases}\text{is continuous at} x = 0\]
Discuss the continuity of \[f\left( x \right) = \begin{cases}2x - 1 & , x < 0 \\ 2x + 1 & , x \geq 0\end{cases} at x = 0\]
For what value of k is the following function continuous at x = 1? \[f\left( x \right) = \begin{cases}\frac{x^2 - 1}{x - 1}, & x \neq 1 \\ k , & x = 1\end{cases}\]
For what value of k is the function
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
In each of the following, find the value of the constant k so that the given function is continuous at the indicated point; \[f\left( x \right) = \begin{cases}\frac{x^2 - 25}{x - 5}, & x \neq 5 \\ k , & x = 5\end{cases}\]at x = 5
In each of the following, find the value of the constant k so that the given function is continuous at the indicated point; \[f\left( x \right) = \binom{\frac{x^3 + x^2 - 16x + 20}{\left( x - 2 \right)^2}, x \neq 2}{k, x = 2}\]
Find the values of a and b so that the function f(x) defined by \[f\left( x \right) = \begin{cases}x + a\sqrt{2}\sin x , & \text{ if }0 \leq x < \pi/4 \\ 2x \cot x + b , & \text{ if } \pi/4 \leq x < \pi/2 \\ a \cos 2x - b \sin x, & \text{ if } \pi/2 \leq x \leq \pi\end{cases}\]becomes continuous on [0, π].
Discuss the continuity of the function \[f\left( x \right) = \begin{cases}2x - 1 , & \text { if } x < 2 \\ \frac{3x}{2} , & \text{ if } x \geq 2\end{cases}\]
If \[f\left( x \right) = \left| \log_{10} x \right|\] then at x = 1
If the function \[f\left( x \right) = \begin{cases}\left( \cos x \right)^{1/x} , & x \neq 0 \\ k , & x = 0\end{cases}\] is continuous at x = 0, then the value of k is
The points of discontinuity of the function
\[f\left( x \right) = \begin{cases}2\sqrt{x} , & 0 \leq x \leq 1 \\ 4 - 2x , & 1 < x < \frac{5}{2} \\ 2x - 7 , & \frac{5}{2} \leq x \leq 4\end{cases}\text{ is } \left( \text{ are }\right)\]
Write an example of a function which is everywhere continuous but fails to differentiable exactly at five points.
Discuss the continuity and differentiability of f (x) = e|x| .
Is every differentiable function continuous?
Is every continuous function differentiable?
Let \[f\left( x \right) = \left( x + \left| x \right| \right) \left| x \right|\]
If \[f\left( x \right) = \left| \log_e |x| \right|\]
Find k, if f(x) =`log (1+3x)/(5x)` for x ≠ 0
= k for x = 0
is continuous at x = 0.
Discuss continuity of f(x) =`(x^3-64)/(sqrt(x^2+9)-5)` For x ≠ 4
= 10 for x = 4 at x = 4
Evaluate :`int Sinx/(sqrt(cos^2 x-2 cos x-3)) dx`
Examine the continuity of the following function :
f(x) = x2 - x + 9, for x ≤ 3
= 4x + 3, for x > 3
at x = 3.
If the function f is continuous at x = 0 then find f(0),
where f(x) = `[ cos 3x - cos x ]/x^2`, `x!=0`
If the function f is continuous at x = 2, then find 'k' where
f(x) = `(x^2 + 5)/(x - 1),` for 1< x ≤ 2
= kx + 1 , for x > 2
Let f(x) = `{{:((1 - cos 4x)/x^2",", "if" x < 0),("a"",", "if" x = 0),(sqrt(x)/(sqrt(16) + sqrt(x) - 4)",", "if" x > 0):}`. For what value of a, f is continuous at x = 0?
The number of points at which the function f(x) = `1/(x - [x])` is not continuous is ______.
The number of points at which the function f(x) = `1/(log|x|)` is discontinuous is ______.
Examine the continuity of the function f(x) = x3 + 2x2 – 1 at x = 1
f(x) = `{{:(3x + 5",", "if" x ≥ 2),(x^2",", "if" x < 2):}` at x = 2
f(x) = `{{:(|x - 4|/(2(x - 4))",", "if" x ≠ 4),(0",", "if" x = 4):}` at x = 4
f(x) = `{{:(|x - "a"| sin 1/(x - "a")",", "if" x ≠ 0),(0",", "if" x = "a"):}` at x = a
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:
