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Discuss the continuity of f(x), where f(...

Discuss the continuity of f(x), where `f(x) = underset(n rarr oo)(lim)("sin"(pi x)/(2))^(2n)`

A

f is continuous on [0,2]

B

f is continuous on R~ `{2n , n in I}`

C

f is continuous on R ~ `{(2n+1), n in I}`

D

`lim_( xto 0+) f(x)=1`

Text Solution

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The correct Answer is:
C
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MCGROW HILL PUBLICATION-LIMITS AND CONTINUITY-Exercise (Level 1 Single Correct Answer)
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  3. The value of lim(x to 0) (sqrt(x^2+1)-1)/(sqrt(x^2+16)-4) is

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  4. lim(xtoa^(-))(sqrt(x-b)-sqrt(a-b))/((x^(2)-a^(2))),(agtb) is

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  5. The value of lim(x to oo) (sqrt(x^2+1)-sqrt(x^2-1)) is

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  6. lim(x->oo)x^(3/2)(sqrt(x^3+1)-sqrt(x^3-1))

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  7. The value of f(1) so that f(x)=(e^x-e)//(x-1) is continuous at x =1 is

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  8. The function f(x)=a[x+1] +b [x-1] , (a ne 0 , b ne 0) where [x] is the...

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  9. Let f(x)=[2x^3-6], where [x] is the greatest integer less than or equa...

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  10. Discuss the continuity of f(x), where f(x) = underset(n rarr oo)(lim)(...

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

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  12. If lim(x to 0) [cot (pi//4 + x)]^(1//x) =Ae^2 then the value of A is

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  13. Let f(x)=([1//2+x ]-[1//2])/x , -1 le x le 2 and f(0) =0([x] is great...

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  14. Let f and g functions such that f+g is a continuous function then

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  15. lim(x to 0) ((1+x^2)^(1//3) - (1-2x)^(1//4))/ (x+x^2) is

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  16. The set of all points for which f(x)=|x| |x-1| + 1/( " [ " x+1 " ] ") ...

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  17. Let f(x)={{:(((e^"[x]"-e^"{x}")e^(-x)+A),"," x lt 0),("2 sin {x}"/"tan...

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  18. If lim(x to 0) ((sin 2x)/x^3 +a+ b/x^2)=0 then then value of 3a +b is

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  19. For continuous functions f and g on R, let f(a)=4, f'(a)=6, g(a)=2, g'...

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  20. Let f(x)={{:((sqrt(1+ax)-sqrt(1-ax))/x ,","-1 le x lt 0),((2x+1)/(x-2)...

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