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Show that the function f(x) given by f(...

Show that the function `f(x)` given by `f(x)={(sinx)/x+cosx ,x!=0 and 2,x=0` is continuous at `x=0.`

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RD SHARMA ENGLISH-CONTINUITY-All Questions
  1. Test the continuity of the following function at the origin: f(x)={(|...

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  2. Show that the function f(x) given by f(x)={(xsin(1/x),x!=0),(0,x=0):} ...

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  3. Show that the function f(x) given by f(x)={(sinx)/x+cosx ,x!=0 and 2,...

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  4. Examination the function f(x) given by f(x)={((cosx)/(pi/2-x) ,, x !=...

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  5. Discuss the continuity of the function f(x) given by f(x)={(2-x ,, x<...

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  6. Determine the values of a , b , c for which the function f(x)={((sin(a...

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  7. If f(x)={((1-coskx)/(xsinx) ,, x!=0),(1/2 ,, x=0):} is continuous at x...

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  8. Discuss the continuity of the function of given by f(x)=|x-1|+|x-2| \ ...

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  9. Determine the value of k for which the following function is continuo...

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  10. Let f(x)=|x|+|x-1|, then

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

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  13. Discuss the continuity of the f(x) at the indicated points: f(x)=|x...

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  14. Prove that f(x)=sqrt(|x|-x) is continuous for all xgeq0.

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  15. Given f(x)=1/(x-1). Find the points of discontinuity of the composite ...

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

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  17. Show that the function f(x) given by f(x)={xsin1/x ,x!=0 0,x=0

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  18. Show that the function f(x) given by f(x)={(sinx)/x+cosx ,\ \ x!=0 2,\...

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  19. Examine the function f(t) given by f(t)={(cost)/(pi//2-t);\ \ \ t!=pi/...

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  20. Show that the function f(x) given by f(x)={((e^(1/x)-1)/(e^(1/x)+1), ...

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