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If lim(x->a)(f(x)/(g(x))) exists, then...

If `lim_(x->a)(f(x)/(g(x)))` exists, then

A

`lim_( xto c)` f(x) exist

B

neither `lim_(x to c)` f(x) nor `lim_(x to c)` g(x) may exist

C

`lim_(x to c)` g(x) exist

D

both `lim_(x to c)` f(x) and `lim_(x to c)` g(x) must exist

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • If lim_(x to a) [(f(x))/(g(x))] exists, then which one of the following correct ?

    A
    Both `underset(xtoa)limf(x)andunderset(xtoa)lim g(x)` must exist
    B
    `underset(xtoa)limf(x)` need not exist but `underset(xtoa)limg(x)` must exist
    C
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    D
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  • Consider the following statements : 1. If lim_(xtoa) f(x) and lim_(xtoa) g(x) both exist, then lim_(xtoa) {f(x)g(x)} exists. 2. If lim_(xtoa) {f(x)g(x)} exists, then both lim_(xtoa) f(x) and lim_(xtoa) g(x) must exist. Which of the above statements is /are correct?

    A
    1 only
    B
    2 only
    C
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    D
    Neither 1 nor 2

  • Consider the following statements : 1. If lim_(xtoa)f(x)andlim_(xtoa)g(x) both exits , then lim_(xtoa){f(x)g(x)} exists. 2. If lim_(xtoa){f(x)g(x)} exists , then both lim_(xtoa)f(x)andlim_(xtoa)g(x) must exist . Which of the above statements is /are correct ?

    A
    Only 1
    B
    Only 2
    C
    Both 1 and 2
    D
    Neither 1 nor 2

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