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Show that f(x)={1+x^2,if0lt=xlt=1 and 2-...

Show that `f(x)={1+x^2,if0lt=xlt=1` and 2-x if `x >1` is discontinuous at x=1

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RD SHARMA ENGLISH-CONTINUITY-All Questions
  1. Extend the definition of the following by continuity f(x)=(1-cos7(x...

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  2. Find the value of a for which the function f defined by f(x)={asinpi/...

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  3. Show that f(x)={1+x^2,if0lt=xlt=1 and 2-x if x >1 is discontinuous...

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  4. Discuss continuity of f(x)={{:(x^(2)/2, if 0le x le 1),(2x^(2)-3x+3/2,...

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  5. Examine the continuity of the function f(x)=3x-2,xlt=0, f(x)=x+1,x>...

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  6. Discuss the continuity of the function f(x)=x, \if \x >0, f(x)= 1,\...

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  7. Discuss the continuity of the function f(x)={x/(|x|),x!=0 0,x=0

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  8. If f(x)=(tan(pi/4-x))/(cot2x) for x!=pi/4, find the value which can be...

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  9. Determine the value of a ,b ,c for which the function f(x)={(sin(a+1)x...

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  10. Show that f(x)=(x-|x|)/(2), when \ x!=0 f(x)=2 \ when \ x=0 \ is \ d...

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  11. Find the relationship between a and b so that the function 'f' def...

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  12. If f(x)=(sin3x)/x,w h e nx!=0, f(x)= 1,w h e n x=0 Find whether f(x) i...

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  13. Prove that the function f(x)={(sinx)/x,x<0x+1,xgeq0 is everywhere ...

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

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

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

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

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

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  20. 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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