हिंदी

Examine Continuity of the Function F(X) at X = 0, Where for X≠0 and for X=0 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Examine continuity of the function f(x) at x = 0, where

`f(x) = (10^x + 7^x - 14^x - 5^x)/(1-cos 4x) , " for " x != 0`

`= 10/7 , " for"  x = 0`

उत्तर

`f(0) = 10/7` ....(given)

Since `lim_(x->0) f(x) != f(0)`, f is discontinuous at x = 0.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
2012-2013 (October)

APPEARS IN

संबंधित प्रश्न

if the function

`f(x)=k+x, for x<1`

       `=4x+3, for x>=1`

id continuous at x=1 then k=

(a) 7

(b) 8

(c) 6

(d) -6


If `f(x)=[tan(pi/4+x)]^(1/x), `

           = k                        ,for x=0

is continuous at x=0 , find k.

 


Find a and b, so that the function f(x) defined by

f(x)=-2sin x,       for -π≤ x ≤ -π/2

     =a sin x+b,  for -π/2≤ x ≤ π/2

     =cos x,        for π/2≤ x ≤ π

is continuous on [- π, π]


If f (x) = x 2 + a, for x ≥ 0 ` =2sqrt(x^2+1)+b, ` is continuous at x = 0, find a and b.


If `f(x) =(e^(x^2)-cosx)/x^2`, for x= 0, is continuous at x = 0, find f(0).


Discuss the continuity of the following function, at x = 0.

`f(x)=x/|x|,for x ne0`

`=1,`for `x=0`


If the function `f(x)=(5^sinx-1)^2/(xlog(1+2x))`  for x ≠ 0 is continuous at x = 0, find f (0).


Discuss the continuity of the function 

f(x) = `("log"(2+"x") - "log"(2-"x"))/("tan""x")` , for x ≠ 0

 = 1  for x = 0 at the point x =0


`lim_(x->1) (x^2 - 3x + 2)/(x^2 - 1)` = ?


If f(x) = `(1 - sin x + cos x)/(1 + sin x + cos x)`, for x ≠ π is continuous at x = π, then t(π) = ______.


If f(x) = `(sin(x^2 - x))/x`, x ≠ 0, is continuous at x = 0, then f(0) is ______ 


If f(x) = `{((3^x - e^x)/(tan2x);     x ≠ 0),(1/2(log3 + 1);    x = 0):}` then ______ 


The function `tanx/|x|` ______


lf f(x) = `(20^x + 3^x - 6^x - 10^x)/(1 - cos8x)`, for x ≠ 0

= `(k/16)log(10/3).log2`, for x = 0

is continuous at x = 0, then the value of k is ______ 


If f(x) = `{{:((sqrt(1 - "ax") - sqrt(1 + "ax"))/"x"","   -1 ≤ "x" ≤ 0), ((3x + 1)/(x - 2)","   0 ≤ x ≤ 1):}` is continuous in [-1, 1], then a is equal to ______


Let f(x) = `{{:((tan pix)/(7x)";", x ≠ 0),("k"";", x = 0):}`. If f(x) is continuous at x = 0, then k = ______.


If f(x) = `{{:(4x - 2",", 0 ≤ x ≤ 2),(3x + "k"",", 2 < x ≤ 3):}` is continuous in [0, 3], then the value of k is ______.


If f(x) = x2 + α for x > 0 = `2sqrt(x^2 + 1)` + β for x < 0 is continuous at x = 0 and `f(1/2)` = 2 then α2 + β2 is ______.


If f(x) = `(e^(x^2) - cos x)/x^2`, for x ≠ 0 is continuous at x = 0, then value of (0) is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×