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Consider f (x) = x ^(ln x), and g (x) = ...

Consider `f (x) = x ^(ln x), and g (x) = e ^(2) x.` Let `alpha and beta` be two values of x satisfying `f (x) = g(x)( alpha lt beta)`
`lim _(x to beta) (f (x) -c beta)/(g (x) - beta ^(2))=l` then the value of x -l equals to:

A

`4-e ^(2)`

B

`e %(2)-4`

C

`4-e`

D

`e-4`

Text Solution

Verified by Experts

The correct Answer is:
B
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VIKAS GUPTA (BLACK BOOK) ENGLISH-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (COMPREHENSION TYPE PROBLEMS)
  1. Let f (x)= {{:(x [x] , 0 le x lt 2),( (x-1), 2 le x le 3):} where [x]=...

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  2. Let f (x)= {{:(x [x] , 0 le x lt 2),( (x-1), 2 le x le 3):} where [x]=...

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  3. Let f (x)= {{:(x [x] , 0 le x lt 2),( (x-1), 2 le x le 3):} where [x]=...

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  4. Let f :R to R be a continous and differentiable function such that f (...

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  5. Let f :R to R be a continous and differentiable function such that f (...

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  6. Let f :R to R be a continous and differentiable function such that f (...

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  7. Let f (x) (cos ^(2) x)/(1+ cos +cos ^(2)x )and g (x) lamda tan x+1(1-l...

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  8. Let f (x) = (cos ^(2) x)/(1+ cos x+cos ^(2)x )and g (x) =lamda tan x+(...

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  9. Population evolve to maximize their reproductive potential in the habi...

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  10. Let f and g be two differentiable functins such that: f (x)=g '(1) s...

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  11. Let f and g be two differentiable functins such that: f (x)=g '(1) s...

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  12. Let f and g be two differentiable functins such that: f (x)=g '(1) s...

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  13. Suppose a function f(x) satisfies the following conditions f (x+y) =...

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  14. Suppose a function f(x) satisfies the following conditions f (x+y) =...

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  15. Let f (x) be a polynomial satisfying lim (x to oo) (x ^(4) f (x))/( x ...

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  16. Let f (x) be a polynomial satisfying lim (x to oo) (x ^(4) f (x))/( x ...

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  17. Consider f (x) = x ^(ln x), and g (x) = e ^(2) x. Let alpha and beta b...

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  18. Consider f (x) = x ^(ln x), and g (x) = e ^(2) x. Let alpha and beta b...

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  19. Let f (n) x+ f (n) (y ) = (x ^(n)+y ^(n))/(x ^(n) y ^(n))AA x, y in R-...

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  20. Let f (n) x+ f (n) (y ) = (x ^(n)+y ^(n))/(x ^(n) y ^(n))AA x, y in R-...

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