हिंदी

The function f(x) = |x| + |x – 1| is ______. - Mathematics

Advertisements
Advertisements

प्रश्न

The function f(x) = |x| + |x – 1| is ______.

विकल्प

  • Continuous at x = 0 as well as at x = 1

  • Continuous at x = 1 but not at x = 0

  • Discontinuous at x = 0 as well as at x = 1

  • Continuous at x = 0 but not at x = 1

MCQ
रिक्त स्थान भरें

उत्तर

The function f(x) = |x| + |x – 1| is continuous at x = 0 as well as at x = 1.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Continuity And Differentiability - Solved Examples [पृष्ठ १०४]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
अध्याय 5 Continuity And Differentiability
Solved Examples | Q 29 | पृष्ठ १०४

वीडियो ट्यूटोरियलVIEW ALL [4]

संबंधित प्रश्न

Examine the following function for continuity:

`f(x) = (x^2 - 25)/(x + 5), x != -5`


Discuss the continuity of the function f, where f is defined by `f(x) = {(-2,"," if x <= -1),(2x, "," if -1 < x <= 1),(2, "," if x > 1):}`


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): 

\[f\left( x \right) = \begin{cases}\frac{\left| x^2 - 1 \right|}{x - 1}, for & x \neq 1 \\ 2 , for & x = 1\end{cases}at x = 1\]

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

\[f\left( x \right) = \binom{\left| x - a \right|\sin\left( \frac{1}{x - a} \right), for x \neq a}{0, for x = a}at x = a\] 

Determine the value of the constant k so that the function 

\[f\left( x \right) = \left\{ \begin{array}{l}\frac{x^2 - 3x + 2}{x - 1}, if & x \neq 1 \\ k , if & x = 1\end{array}\text{is continuous at x} = 1 \right.\] 


For what value of k is the function 

\[f\left( x \right) = \begin{cases}\frac{\sin 5x}{3x}, if & x \neq 0 \\ k , if & x = 0\end{cases}\text{is continuous at x} = 0?\]


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


Discuss the continuity of the f(x) at the indicated points:  f(x) = | x − 1 | + | x + 1 | at x = −1, 1.

 

For what value of k is the following function continuous at x = 2? 

\[f\left( x \right) = \begin{cases}2x + 1 ; & \text{ if } x < 2 \\ k ; & x = 2 \\ 3x - 1 ; & x > 2\end{cases}\]

Find all point of discontinuity of the function 

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

The function  \[f\left( x \right) = \begin{cases}\frac{e^{1/x} - 1}{e^{1/x} + 1}, & x \neq 0 \\ 0 , & x = 0\end{cases}\]

 


If \[f\left( x \right) = \begin{cases}mx + 1 , & x \leq \frac{\pi}{2} \\ \sin x + n, & x > \frac{\pi}{2}\end{cases}\] is continuous at \[x = \frac{\pi}{2}\]  , then

 


Discuss the continuity and differentiability of f (x) = |log |x||.


Is every continuous function differentiable?


If f (x) is differentiable at x = c, then write the value of 

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

If \[f\left( x \right) = \left| \log_e x \right|, \text { then}\]


`f(x)=(x^2-9)/(x - 3)` is not defined at x = 3. what value should be assigned to f(3) for continuity of f(x) at = 3?


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.


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.


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)


f(x) = `{{:(|x - "a"| sin  1/(x - "a")",",  "if"  x ≠ 0),(0",",  "if"  x = "a"):}` at x = a


Write the number of points where f(x) = |x + 2| + |x - 3| is not differentiable.


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):}`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×