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Assertion (A) : Lt(x to 0)(|x|)/(x)=1 ...

Assertion (A) : `Lt_(x to 0)(|x|)/(x)=1`
Reason (R) : Limit of a function doesn't exist if left and right limits exists and are not equal the correct answer is

A

Both A and R are true and R is the correct explanation of A

B

Both A and R are true and R is not the correct explanation of A

C

A is true but R is false

D

A is false but R is true

Text Solution

Verified by Experts

The correct Answer is:
D
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Show that Lt_(xto0)(|x|)/x does not exist.

If f(x) = (|x|)/x then show that Lt_(x to 0) f(x) does not exist.

Knowledge Check

  • Assertion (A) : Lt_(x to0) (x)/(1+e^((1)/(x)))=0 Reason(R) : As x to 0, e^(1//x) to0 and x to 0+,e^(-1//x) to 0

    A
    Both (A) and (R) are true and (R) is the correct explanation of (A)
    B
    Both (A) and (R) are true and (R) is not the correct explanation of (A)
    C
    (A) is true but (R) is false
    D
    (A) is false but (R) is true
  • Assertion (A) : Lt_(x to 2) sqrt(2-x)=0 Reason (R) : If a function f is defined only on (a-delta,a) for delta gt 0 then Lt_(x to a)-f(x)=Lt_(x to a)f(x)

    A
    Both (A) and (R) are true and (R) is the correct explanation of (A)
    B
    Both (A) and (R) are true and (R) is not the correct explanation of (A)
    C
    (A) is true but (R) is false
    D
    (A) is false but (R) is true
  • Assertion (A) : f(x) = (1)/( 1 + e^(1//e))(x ne 0) " and " f(0) = 0 is right continuous at x = 0 Reason (R) : underset(x to 0+)(Lt ) (1)/(1 + e^(1//x)) = 0 The correct answer is

    A
    Both (A) and (R) are true and (R) is the correct explanation of (A)
    B
    Both (A) and (R) are true and (R) is not the correct explanation of (A)
    C
    (A) is true but (R) is false
    D
    (A) is false but (R) is ture
  • Similar Questions

    Explore conceptually related problems

    Show that Lt_(xto0)(|sinx|)/x does not exist.

    Show that Lt_(x to2)([x]+x) does ot exists.

    If f(x)={{:(2x+3"if", x le0),(3(x+1)"if",x gt theta):} Find left and right hand limits and choose whether f(x) has limit at the point x=0 .

    if f(x)={{:(x^(2), if x le),(x, if1 lt x le2),(x-3,if x gt2):} Find the left and right hand limits and check wheather f(x) has limit at the point x=1:2

    I. underset(x to 0)"Lt "sqrts does not exist II. underset(x to 1)"Lt" (|x|)/(x) does not exist.