Home
Class 11
MATHS
Suppose f(x)={:{(a+bx,x lt 1) ,(4,x=1), ...

Suppose `f(x)={:{(a+bx,x lt 1) ,(4,x=1), (b-ax,x gt 1):}` and if `lim_(x to 1) f(x)=f(1).` What are possible values of a and b?

Text Solution

Verified by Experts

The correct Answer is:
a=0 b=4
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS - LIMITS AND CONTINUITY

    FULL MARKS|Exercise EXERCISE 9.1|24 Videos

  • DIFFERENTIAL CALCULUS - LIMITS AND CONTINUITY

    FULL MARKS|Exercise EXERCISE 9.2|15 Videos

  • DIFFERENTIAL CALCULUS - LIMITS AND CONTINUITY

    FULL MARKS|Exercise EXERCISE 9.6|25 Videos

  • DIFFERENTIAL CALCULUS - DIFFERENTIABILITY AND METHODS OF DIFFERENTIATION

    FULL MARKS|Exercise EXERCISE 5 ADDITIONAL PROBLEMS (Find the derivative of following functions.)|10 Videos

  • EXAMINATION QUESTION PAPER - JUNE 2019

    FULL MARKS|Exercise PART -IV|7 Videos

Similar Questions

Explore conceptually related problems

Let f(x)={{:(a+bx","xlt1),(4","x=1),(b-ax","xgt1):} and if lim_(xto1)f(x)=f(1) what are the possible values of a and b

Suppose f(x)={{:(a+bx",",xlt1),(4",",x-1),(b-ax",",xgt1):} and if lim_(xrarr1)f(x)=f(1) what are possible values of a and b?

Knowledge Check

  • f(x)={(x,if,0,le,x,lt,1),(1,if,x,ge,1):} then f'(1) is:

    A
    1
    B
    0
    C
    `1/2`
    D
    Does not exist

  • IF f(x)=int_1^x (e^(sinu))/u du,x gt 1 and int_1^3 e^(sinx^2)/xdx=1/2[f(a)-f(1)] then one of the possible value of a is

    A
    3
    B
    6
    C
    9
    D
    5

    • Similar Questions

    Explore conceptually related problems

    If f(x)={:{(2x+1,x le 0),(3(x+1),x gt 0):} . Find lim_(x to 0) f(x) and lim_(x to 1) f(x) .

    Let f(x)={:{(x+1,x gt 0),(x-1,x lt 0):}

    Given that f(x) = {{:(sqrt(x-1),x ge 1),(4,x lt 1):}} . Find f(0)

    Given that f(x) = {{:(sqrt(x-1),x ge 1),(4,x lt 1):}} . Find f(3)

    Let f:""RrarrR be defined by f(x)""= {(k-2x , if xle-1),( 2x+3, if x gt-1):} . If f has a local minimum at x""=""1 , then a possible value of k is (1) 0 (2) -1/2 (3) -1 (4) 1

    The function f(x) = {{:(2, x lt=1),(x , x gt 1 ):} is not differentiable at ………..

    Home
    Profile