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If f(x) = (1)/(2) x - 1, then on the int...

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

A

tan [f(x)] is continuous but `(1)/(f(x))` is not

B

tan [f(x)] and `f^(-1) (x)` are both continuous

C

tan [f(x)] and `(1)/(f(x))` are both continuous

D

tan [f(x)] and `(1)/(f(x))` are both discontinuous

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The correct Answer is:
D
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MODERN PUBLICATION-LIMIT AND CONTINUITY -MULTIPLE CHOICE QUESTIONS(LEVEL - II )
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  2. To make f(x)=(x+1)^(cotx) continuous at x=0,f(0) must defined as

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

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

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  5. Let f(x) = (tan ((pi)/(4) - x))/(cot 2 x), x ne pi//4, the value which...

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

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  7. Let the function f be defined by f(x) = "x sin" (1)/(x), when x ne 0 =...

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

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  9. The value of f(0) for which the function : (log(e) (1-ax) - log(3) (1-...

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  10. If f(x) = ((e^(x)-1)^(4))/(sin((x^(2))/(lambda^(2)))log(1+(x^(2))/(2))...

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  11. If f(x) = [x] + [-x], x ne 2 = lambda, x = 2, then f is continuous at ...

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  12. Let f(x) be defined by f(x) = {{:((|x^(2) - x|)/(x^(2) - x),x ne 0"," ...

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  13. lim(x rarr oo) ((x^(2) + 5x + 3)/(x^(2) + x + 2))^(x) is :

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  14. lim(x rarr 0) (log (3 + x) - log(3 - x))/(x) = k, the value of k is :

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  15. lim(x rarr (pi)/(2)) ((1 - tan x//2)(1-sin x))/((1+tan x//2) (pi - 2x)...

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  16. The value of lim(x rarr 0) (int(0)^(x^(2))sec^(2)t dt)/(x sin x) is :

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  17. The value of lim(n rarr oo) (1 + 2^(4) + 3^(4) +…...+n^(4))/(n^(5)) - ...

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  18. lim(x rarr 0) (sin nx[(a-n)nx - tan x])/(x^(2)) = 0, where n is non-ze...

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  19. If lim(h rarr 0) (1 + (a)/(x) + (b)/(x^(2)))^(2x) = e^(2), then the va...

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  20. Let f(x) = (1-tanx)/(4x-pi),x ne (pi)/(4), x in [0, (pi)/(2)], if f(x)...

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