मराठी

Y = |x – 1| is a continuous function. - Mathematics

Advertisements
Advertisements

प्रश्न

y = |x – 1| is a continuous function.

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर

उत्तर

This statement is True.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Continuity And Differentiability - Solved Examples [पृष्ठ १०६]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 5 Continuity And Differentiability
Solved Examples | Q 43 | पृष्ठ १०६

व्हिडिओ ट्यूटोरियलVIEW ALL [4]

संबंधित प्रश्‍न

Examine the continuity of the following function :

`{:(,,f(x)= x^2 -x+9,"for",x≤3),(,,=4x+3,"for",x>3):}}"at "x=3`


Discuss the continuity of the following functions at the indicated point(s): (iv) \[f\left( x \right) = \left\{ \begin{array}{l}\frac{e^x - 1}{\log(1 + 2x)}, if & x \neq a \\ 7 , if & x = 0\end{array}at x = 0 \right.\]


Discuss the continuity of the following functions at the indicated point(s): 

\[f\left( x \right) = \left\{ \begin{array}{l}\frac{1 - x^n}{1 - x}, & x \neq 1 \\ n - 1 , & x = 1\end{array}n \in N \right.at x = 1\]

Determine the value of the constant k so that the function

\[f\left( x \right) = \begin{cases}k x^2 , if & x \leq 2 \\ 3 , if & x > 2\end{cases}\text{is continuous at x} = 2 .\]


Discuss the continuity of the f(x) at the indicated points: 

(i) f(x) = | x | + | x − 1 | at x = 0, 1.


If the functions f(x), defined below is continuous at x = 0, find the value of k. \[f\left( x \right) = \begin{cases}\frac{1 - \cos 2x}{2 x^2}, & x < 0 \\ k , & x = 0 \\ \frac{x}{\left| x \right|} , & x > 0\end{cases}\] 

 


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?

 


Given the function  
\[f\left( x \right) = \frac{1}{x + 2}\] . Find the points of discontinuity of the function f(f(x)).

Find all point of discontinuity of the function 

\[f\left( t \right) = \frac{1}{t^2 + t - 2}, \text{ where }  t = \frac{1}{x - 1}\]

Find f (0), so that  \[f\left( x \right) = \frac{x}{1 - \sqrt{1 - x}}\]  becomes continuous at x = 0.

 


If  \[f\left( x \right) = \begin{cases}\frac{{36}^x - 9^x - 4^x + 1}{\sqrt{2} - \sqrt{1 + \cos x}}, & x \neq 0 \\ k , & x = 0\end{cases}\]is continuous at x = 0, then k equals

 


If  \[f\left( x \right) = \begin{cases}\frac{\sin \left( \cos x \right) - \cos x}{\left( \pi - 2x \right)^2}, & x \neq \frac{\pi}{2} \\ k , & x = \frac{\pi}{2}\end{cases}\]is continuous at x = π/2, then k is equal to


Discuss the continuity and differentiability of 

\[f\left( x \right) = \begin{cases}\left( x - c \right) \cos \left( \frac{1}{x - c} \right), & x \neq c \\ 0 , & x = c\end{cases}\]

Is every differentiable function continuous?


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 

\[\lim_{x \to c} f \left( x \right)\]

Write the points where f (x) = |loge x| is not differentiable.


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`


Find the value of k for which the function f (x ) =  \[\binom{\frac{x^2 + 3x - 10}{x - 2}, x \neq 2}{ k , x^2 }\] is continuous at x = 2 .

 
 

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


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 = I, then find f(1), where f(x) = `(x^2 - 3x + 2)/(x - 1),` for x ≠ 1


If Y = tan-1 `[(cos 2x - sin 2x)/(sin2x + cos 2x)]` then find `(dy)/(dx)`


If the function
f(x) = x2 + ax + b,         x < 2

      = 3x + 2,                 2≤ x ≤ 4

      = 2ax + 5b,             4 < x

is continuous at x = 2 and x = 4, then find the values of a and b


f(x) = `{{:(3x + 5",", "if"  x ≥ 2),(x^2",", "if"  x < 2):}` at x = 2


f(x) = `{{:(3x - 8",",  "if"  x ≤ 5),(2"k"",",  "if"  x > 5):}` at x = 5


f(x) = `{{:((sqrt(1 + "k"x) - sqrt(1 - "k"x))/x",",  "if" -1 ≤ x < 0),((2x + 1)/(x - 1)",",  "if"  0 ≤ x ≤ 1):}` at x = 0


Examine the differentiability of f, where f is defined by
f(x) = `{{:(x[x]",",  "if"  0 ≤ x < 2),((x - 1)x",",  "if"  2 ≤ x < 3):}` at x = 2


If f(x) = `{{:("m"x + 1",",  "if"  x ≤ pi/2),(sin x + "n"",",  "If"  x > pi/2):}`, is continuous at x = `pi/2`, then ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×