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Let f(x) = [{:(5^(1//x),x lt 0),(lambda[...

Let `f(x) = [{:(5^(1//x),x lt 0),(lambda[x],x le 0","lambda in R):}`, then at x = 0 :

A

f is continuous whatever `lambda` may be

B

f is discontinuous

C

f is continuous only if `lambda = 0`

D

None of these

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The correct Answer is:
A
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MODERN PUBLICATION-LIMIT AND CONTINUITY -MULTIPLE CHOICE QUESTIONS(LEVEL - II )
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  6. The function f(x) = [x] is :

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  9. Let f(x) = (tan (pi//4-x))/(cot 2x)"for x" ne pi//4, then for f to be ...

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  11. The value of f(0) so that the function : f(x) = (sqrt(1 + x) - (1+x)^(...

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  12. Let f(x) = (sqrt(1 + sin x)-sqrt(1-sin x))/(x)lim The value, which sho...

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  13. To make f(x)=(x+1)^(cotx) continuous at x=0,f(0) must defined as

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  14. If f(x) = (1)/(2) x - 1, then on the interval [0, pi] :

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  15. The value of x, where the function : f(x) = (tan x log (x-2))/(x^(2) -...

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  17. Let f(x) = x + 2, where x le 1 and f(x) = 4x - 1, when x gt 1, then :

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  19. f(x) = (|x-a|)/(x-a), when x ne a, = 1, when x = a, then :

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