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If f(x) = "min"{1, x^2, x^3} then :...

If `f(x) = "min"{1, x^2, x^3}` then :

A

f(x) is continuous everyone

B

f(x) is continuous and differentiable everywhere

C

f(x) is not differentiable at two points

D

f(x) is not differentiable at one point

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The correct Answer is:
A, D
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PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
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  2. Which of the following functions are continuous on (0, pi):

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  3. If f(x) = "min"{1, x^2, x^3} then :

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  4. Let f(x) be defined in [-2, 2] by f(x) = "maximum" (sqrt(4-x^2), sqr...

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  5. If lim(x rarr 0)((a^x+b^x+c^x)/3)^(lambda/x), (a, b, c, lambda gt o) i...

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  6. If f(x)=(|x|/(2 + |x|))^(2x), then

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  7. Let f(x) = {(1+(2x)/lambda, o le x le 1), (lambda x, 1 le x le 2):} ...

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  8. If m, n in N, lim x tends to 0 '(sin(x^m)/sin(x^n))​' (m, n∈N)=0, lf

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  9. Let f(x) = (1-cos4x)/x^2, g(x) sqrtx/(sqrt(16+sqrtx)-4) and phi(x) ...

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  10. Let f(x) = (1-cos4x)/x^2, g(x) sqrtx/(sqrt(16+sqrtx)-4) and phi(x) ...

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  14. Match List - I with List-II

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  15. Let f and g be two continuous and let h be defined as h(x) = lim(n r...

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  16. If lim(x rarr 5)((x^k - 5^k)/(x - 5)) = 500, then k is equal to

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  17. Evaluate the following limits (if exists), where {,} denotes the fract...

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  19. Evaluate the following limits (if exists), where {,} denotes the fract...

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  20. Evaluate the following limits (if exists), where {,} denotes the fract...

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