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

What is `lim_(xto0) (a^(x)-b^(x))/(x)` equal to?

A

ln (ab)

B

`(lna)/(lnb)`

C

`ln((a)/(b))`

D

`ln((b)/(a))`

Text Solution

Verified by Experts

The correct Answer is:
C

Consider
`underset(xto0)lim(a^(x)-b^(x))/(x )=underset(xto0)lim(a^(x)loga-b^(x)logb)/(1)`
(Using L' Hospital's rule)
`=loga-logb=log""(a)/(b)`
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NDA PREVIOUS YEARS-FUNCTIONS, LIMIT, CONTINUITY AND DIFFERENTIABILITY-MCQs
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  2. If f(x)=2x+7andg(x)=x^(2)+7,x""inR, then what are values of x for whic...

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  3. What is lim(xto0) (a^(x)-b^(x))/(x) equal to?

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  4. If the function f(x)=(x(x-2))/(x^(2)-4),xnepm2 is continuous at x=...

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  5. At how many points is the fucntion f(x)=[x] discontinuous?

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  6. If f(x)=(2)/(3)x+(3)/(2),x""inR, then what is f^(-1)(x) equal to ?

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  7. What is lim(xtooo) (sqrt(a^(2)x^(2)ax+1)sqrt(a^(2)x^(2)+1)) equal to?

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  8. What is the value of k for which the following fucntion f(x) is contin...

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  9. Which one of the following is correct in respect of the function f(x)=...

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  10. Consider the following statements: I. f(x)=|x-3| is continuous at x=...

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  11. What is lim(xto0) x^(2)sin((1)/(x)) equal to?

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  12. What is lim(xto-2)((1+2)/(x^(3)+8))

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  13. If f(x)f[xy]=f[x]f[y] then f[t] may be of the form:

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  14. Which one of the following functions is differentiable for all real va...

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  15. What is lim(xto0) (sqrt(1+x-1))/(x)

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  16. What is lim(xto0) (2(1-cosx))/(x^(2) equal to?

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  17. Consider the following : 1. lim(xto0) (1)/(x) exists. 2. lim(xto0)...

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  18. Which one of the following is correct in respect of the function f(x)=...

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  19. What is lim(xto2) (x-2)/(x^(2)-4) equal to?

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  20. Let f:RtoR be a function whose inverse is (x+5)/(3). What is f(x) equa...

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