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The value of a for which the function f...

The value of a for which the function `f(x)=f(x)={((4^x-1)hat3)/(sin(x a)log{(1+x^2 3)}),x!=0 12(log4)^3,x=0` may be continuous at `x=0` is 1 (b) 2 (c) 3 (d) none of these

A

1

B

2

C

3

D

none of these

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D
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ML KHANNA-LIMITS, CONTINUITY AND DIFFERENTIABILITY -PROBLEM SET (2) (MULTIPLE CHOICE QUESTIONS)
  1. The function f(x) = {{:(x^(2)//a, 0 le x lt 1),(a, 1 le x lt sqrt(2)),...

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  2. If f(x) = x^(a) log x and f(0) = 0 then the value of alpha for which ...

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  3. The value of a for which the function f(x)=f(x)={((4^x-1)hat3)/(sin(x...

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  4. If f(x) =(e^(x)-1)^(4)/(sin(x^(2)/lambda^(2))log (1+x^(2)/2)), x ne 0 ...

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  5. Let f(x) = (x(1+ a cos x) - b sinx)/x^(3), x ne 0 f(0) = 1. If f(x) is...

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  6. f(x) = {{:((1- cos 4x)/x^(2), x lt 0),(=a, x =0),(=sqrt(x)/(sqrt(16+sq...

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  7. The function f(x) = {{:(x + asqrt(2) sin x, 0 le x lt pi//4),(2x cotx ...

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  8. In order that the function f(x) = (x+1)^(cot x) is continuous at x=0...

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  9. Function f(x) = (sin 2x)^(tan^(2)2x) is not defined at x=pi/4. If f(x...

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  10. Let f(x)=(tan(pi/4-x))/(cot2x),x!=pi/4 . The value which should be ass...

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  11. If f(x) = (2-(256 -7x)^(1//8))/((5x+32)^(1//5)-2), (x ne 2), then for ...

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  12. The value of lambda that makes the function f(x) = {{:((cos x)^(1//sin...

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  13. Let f''(x) be continuous at x = 0 and f''(0)=4, Then value of lim(x t...

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  14. If the function f(x) = {{:((1+ |sin x|^(a/(sin x))), -pi//6 lt x lt 0)...

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  15. Let f(x) = {{:(-2 sin x, x le -pi//2),(a sin x + b, -pi//2 lt x lt pi/...

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  16. The value of f(0) so that the function f(x) = (2x - sin^(-...

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  17. If f(x) = {{:((36^(x) - 9^(x) -4^(x)+1)/(sqrt(2)- sqrt(1+ cos x)), x n...

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  18. Let f(x) ={{:((x-4)/(|x-4|)+a, x lt 4),((x-4)/(|x-40|)+b, x gt 4):}, T...

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  19. If f(x)={1/((pi-2x)^2)dot(logsinx)/((log(1+pi^2-4pix+4x^2)),x!=pi/2k ...

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  20. If f(x) = {{:((sin (a+1) x + sinx)/x, x lt 0),((sqrt(x+bx^(2))- sqrt(x...

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