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Test the continuity of the following function at the origin; `f(x)={x/(|x|),x!=0 and 1,x=0`

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RD SHARMA ENGLISH-CONTINUITY-All Questions
  1. Let f(x)=(1-cosx)/(x^2),\ \ \ w h e n\ x!=0,\ f(x)=1,\ \ \ w h e n\ x...

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  2. If f(x)={e^(1/x) ,1 ifx!=0ifx=0 Find whether f is continuous a...

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  3. Test the continuity of the following function at the origin; f(x)={x...

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  4. The function f(x)={(x^2/a, if 0le x lt1),(a, if 1 le x lt sqrt2),((2b^...

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  5. A function f(x) is defined as f(x)={(x^2 -x-6)/(x-3);ifx!=3 and 5ifx=...

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  6. Find the domain of f(x) = sin^-1 x+ cos x

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  7. If y=(x-1)log(x-1)-(x+1)log(x+1), prove that : dy/dx = log((x-1)/(1+x)...

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  8. The value of f(0) , so that the function f(x)=(sqrt(a^2-a x+x^2)-sqrt(...

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  9. The value of a for which the function f(x) = {[5x-4,if 0ltxle1],[4x^2...

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  10. Evaluate : tan(cos^-1(-7/25))

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  11. The function f(x)=tanx is discontinuous on the set {npi; n in Z} (b)...

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  12. If f(x)=|(log)(10)x| , then at x=1 f(x) is continuous and f^(prime)(1...

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  13. If the function f(x)={(cosx)^(1/x),x!=0k ,x=0 is continuous at x=0 , t...

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  14. If f(x)=(x+1)^(cotx) be continuous at x=0, the f(0) is equal to (a...

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  15. If f(x)={m x+1,xlt=pi/2sinx+n ,x &gt;pi/2 is continuous at x=pi/2, t...

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  16. If f(x)={((36^x-9^x-4^x+1)/(sqrt(2)-sqrt(1+cosx)),x!=0),(k ,x=0)) is ...

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  17. If f(x)={(1-cos10x)/(x^2a),x<0(sqrt(x))/(sqrt(625)+sqrt(x)-25),x >0,x=...

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  18. If f(x)={((sin(cosx)-cosx)/((pi-2x)^2) ,, x!=pi/2),(k ,, x=pi/2):} is ...

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  19. Discuss the continuity of the function f(x) given by f(x)={2x-1,ifx...

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

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