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If f(x) = {((1-cos 4x)/x^(2), x lt 0),(a...

If `f(x) = {((1-cos 4x)/x^(2), x lt 0),(a, x =0),((sqrtx)/(sqrt(16+sqrt(x))-4), xgt 0):}` then the value of a for which f(x) is continuous at x = 0 is

A

5

B

8

C

4

D

3

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The correct Answer is:
B
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HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
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  2. Let f(x+y) = f(x).f(y), forall, x, y. Suppose f(5) =2, f^(')(0) = 3 th...

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  3. If f(x) = {((1-cos 4x)/x^(2), x lt 0),(a, x =0),((sqrtx)/(sqrt(16+sqrt...

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  4. The value of lim(x rarr 0) (sqrt(a+x)- sqrt(a-x))/x =

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  5. The value of Lim(xto pi)(sqrt(2+cosx)-1)/((pi-x)^(2)) is

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  6. If f (x) = |{:( sin x , cos x , tan x) , (x^(3) , x^(2) , x) , (2x , 1...

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  7. If f(a)=2,f'(a)=1,g(a)=-3,g'(a)=-1 then Lim(xtoa)(f(a)g(x)-f(x)g(a))/(...

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  8. lim(x rarr 0) (1-ax)^(1/x) =

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  9. Lim(nto oo)(3^(n)+4^(n))^((1)/(n))=

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  10. lim(x rarr oo) (1-4/(x-1))^(3x-1) =

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  12. lim(theta rarr pi/2) (pi/2- theta)/(cot theta) =

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  13. lim(x rarr 0) (tan x - sin x)/(x^(3)) =

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  14. The value of lim(x to 0)(5^(x)-5^(-x))/(2x)=

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  15. lim(x-1)(tan(x^(2)-1))/(x-1) is equal to

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  17. If G(x) = -sqrt(25-x^(2)) the lim(x rarr 1) (G(x)-G(1))/(x-1) =

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  18. lim(n rarr oo) ((1)/(1-n^(2)) + (2)/(1-n^(2)) +…...+(n)/(1-n^(2))) is ...

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  19. lim(x rarr oo) ((2 + x)^(40) (4 + x)^(5))/((2-x)^(45)) is :

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