Home
Class 12
MATHS
If f(x)={{:((log x-log3)/(x-3),"for "x n...

If `f(x)={{:((log x-log3)/(x-3),"for "x ne 3),(c,"for "x =3):}` is continuous at x = 3, then the value of c is

A

3

B

2

C

`(1)/(3)`

D

`(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given `f(x)={((logx-log3)/(x-3)",",x ne 3),(C",",x =3):}`
Since f(x) is continuous at x = 3
`therefore f(3)=lim_(x to 3)f(x)`
`rArr C=lim_(x to 3) (logx-log 3)/(x-3)=lim_(x to 3) ((1)/(x))/(1)" " `[by L' Hospital's rule]
`=(1)/(3)`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2 (MISCELLANEOUS PROBLEMS)|60 Videos

  • CONTINUITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|16 Videos

  • CIRCLE AND CONICS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise All Questions|74 Videos

  • DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|22 Videos

Similar Questions

Explore conceptually related problems

If f(x)={(log_((1-3x))(1+3x)",","for",x ne 0),(k",","for",x =0):} is continuous at x = 0, then k is equal to

If {:(f(x),=log_(1-3x)(1+3x),",",x != 0),(,=k, ",",x = 0):} is continuous at x = 0, then the value of k is

If f(x) {:(=(log (1-2x)-log(1-3x))/x", " x != 0 ),(=a", " x = 0 ):} is continuous at x = 0 , then : a =

If f(x) {:(=(log (1+3x )-log(1-2x))/x", if " x != 0 ),(=a", if " x =0 ):} is continuous at x = 0 , then a =

If f(x)={{:(((5^(x)-1)^(3))/(sin((x)/(a))log(1+(x^(2))/(3)))",",x ne0),(9(log_(e)5)^(3)",",x=0):} is continuous at x=0 , then value of 'a' equals

If f(x)={(log_(1-3x)(1+3x), x!=0),(=k ,x=0)) is continuous at x=0, then value of k equals (A) -1 (B) 1 (C) 2 (D) -2

If f(x)={((log(1+x)-log(1-x))/(x)"," , "when " x ne 0),(3"," , "when " x = 0):} is

If 3log_(2)x+log_(2)27=3 then the value of x is