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What is lim(x to 0) (1-sqrt(1+x))/(x) eq...

What is `lim_(x to 0) (1-sqrt(1+x))/(x)` equal to?

A

`1//2`

B

`-1//2`

C

1

D

-1

Text Solution

Verified by Experts

The correct Answer is:
A
Consider `underset(xto0)lim(1-sqrt(1+x))/(x)`
`=underset(xto0)lim(1-(1+x))/(x(1+sqrt(1+x)))("By Rattionalizing")`
`=underset(xto0)lim(-x)/(x(1+sqrt(1+x)))=(-1)/(2)`
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NDA PREVIOUS YEARS-FUNCTIONS, LIMIT, CONTINUITY AND DIFFERENTIABILITY-MCQs
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  2. lim(x to 0) (sinx-tanx)/(x) equal to?

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  4. Consider the following statements: 1. The derivative where the funct...

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  5. Let N be the set of natural numbers and f : N->N be a function given b...

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  6. Let f be a function from the set of natural numbers to the set of even...

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  7. Consider the following function : 1. f(x)=e^(x),"where "xgt0 2. g(...

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  8. What is lim(x to 2) (2-x)/(x^(3)-8) equal to ?

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  9. A function f:RtoR is defined as f(x)=x^(2)" for "xge0,f(x)=-x" for "xl...

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  10. What is lim(xto0) (1-cosx)/(x) equal to ?

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  11. What is lim(xto0) (cosx)/(pi-x) equal to ?

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  12. What is lim(xto0) (sin2x+4x)/(2x+sin4x) equal to ?

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  13. Let N denote the set of all non-negative integers and Z denote the set...

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  14. What is lim(xto0) ((1+x)^(n)-1)/(x) equal to ?

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  15. What is lim(xto0) (x)/(sqrt(1-cosx)) equal to ?

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  16. What is underset(xrarr(pi)/(2))limf(x)=underset(xrarr(pi)/(2))lim(1-si...

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  17. What is the value of lamda if the function is continuous at x=(pi)/(2)...

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  18. If f(9)=9andf'(9)=4 then what is lim(xto9) (sqrtf(x)-3)/(sqrtx-4) equa...

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  19. Consider the following statements : 1. The function f(x)=3sqrtx is...

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