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If lim(x to a) [(f(x))/(g(x))] exists, t...

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

Both `underset(xtoa)limf(x)andunderset(xtoa)limg(x)` need not exist

D

`underset(xtoa)limf(x)` must exist but `underset(xtoa)limg(x)` need not exist

Text Solution

Verified by Experts

The correct Answer is:
A
For `underset(xtoa)lim[(f(x))/(g(x))]` to exist, then both `underset(xtoa)limf(x)andunderset(xtoa)limg(x)` must exist.
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NDA PREVIOUS YEARS-FUNCTIONS, LIMIT, CONTINUITY AND DIFFERENTIABILITY-MCQs
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  3. If lim(x to a) [(f(x))/(g(x))] exists, then which one of the following...

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  7. If f(x)=(x+1)^(cotx) is continuous at x=0, then what is f(0) equal to?

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  8. What is the value of lim(xtooo) ((x-2)/(x+2))^(x+2) = ?

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  9. If the derivative of the function f(x) ={ax^2+b , x lt -1 and bx^2 ...

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  11. Consider the cubic equation x^3 + ax^2 + bx + c = 0, where a, b, c are...

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  12. If (x-a)/(b+c)+(x-b)/(c+a)+(x-c)/(a+b)=3 then value of x is

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  13. If -x^(2)+3x+4gt0, then which one of the following is correct?

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  14. Given f(x)=x+(1)/(x), then what is f^(2)(x) equal ot ?

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  15. If f(x)={{:(1,x" is a rational number"),(0",","x is an irrational numb...

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  16. A function f is defined as follows f(x)=x^(p)cos((1)/(x)),xne0 f(0...

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  18. What is lim(xto0)(a^(x)-b^(x))/(x)?

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