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Find f(0) , so that f(x)=x/(1-sqrt(1-x))...

Find `f(0)` , so that `f(x)=x/(1-sqrt(1-x))` becomes continuous at `x=0` .

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RD SHARMA ENGLISH-CONTINUITY-All Questions
  1. Define continuity of a function at a point.

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  2. What happens to a function f(x) at x=a , if (lim)(x->a)f(x)=f(a)

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  3. Find f(0) , so that f(x)=x/(1-sqrt(1-x)) becomes continuous at x=0 .

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  4. The function f(x)={((sin3x)/x ,x!=0),(k/2,x=0):} is continuous of x...

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  5. If the function f(x)=(sin10 x)/x , x!=0 is continuous at x=0 , find f(...

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  6. If f(x)={(x^2-16)/(x-4), if\ x!=4k\ ,if\ x=4 is continuous at x=4 , fi...

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  7. Determine whether f(x)={(sinx^2)/x\ \ \ ,\ \ \ x!=0 0\ \ \ ,\ \ \ x=0 ...

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  8. If f(x)={(1-cosx)/(x^2)\ \ \ ,\ \ \ x!=0k\ \ \ ,\ \ \ x=0 is continuou...

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  9. If f(x)={(sin^(-1)x)/x\ \ \ ,\ \ \ x!=0k\ \ \ ,\ \ \ x=0 is continuous...

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  10. Write the value of b for which f(x)={5x-4,when0 < x <= 1, 4x^2+3bx ,wh...

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  11. The function f(x)=(4-x^2)/(4x-x^3) (a) discontinuous at only one poin...

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  12. If f(x)=|x-a|varphi(x) , where\ varphi(x) is continuous function, t...

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  13. If f(x)=|(log)(10)x|,t h e na tx=1 f(x) is continuous and f^(prime)(1...

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  14. 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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  15. If f(x) defined by f(x)={(|x^2-x|)/(x^2-|x|),x!=0,1-1. Then (A)f...

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

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

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  18. If f(x)={(log(1+a x)-log(1-b x))/x\ \ \ ,\ \ \ x!=0,\ \ \ \ \ \ \k\ \ ...

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  19. The function f(x)={(e^(1/x)-1)/(e^(1/x)+1),x!=0 \ \ \ \ \ \ \ 0,x=0 ...

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  20. Let f(x)={(x-4)/(|x-4|)+a ,x<4 \ \ \ \ \a+b , x=4 \ \ \ \ \ \ ,(x-4)/...

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