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Prove that lim(x->a^+) [x]=[a] for all ...

Prove that `lim_(x->a^+) [x]=[a]` for all `a in R,` where [*] denotes the greatest integer

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RD SHARMA ENGLISH-LIMITS-All Questions
  1. Suppose f(x)={(a+bx, x<1), (4, x=1), (b-ax, x>1):} and if lim(xto1) f(...

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  2. Find the left hand and right hand limits of greatest integer function ...

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  3. Prove that lim(x->a^+) [x]=[a] for all a in R, where [*] denotes the ...

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  4. If f is an even function, then prove that lim(x->0^-) f(x) = lim(x->0^...

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  5. Show that ("lim")(x->0)x/(|x|) does not exist.

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  6. Find k so that ("lim")(x->2)\ f(x) may exist, where f(x)={2x+3,\ xlt=2...

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  7. Show that ("lim")(x->0)1/x does not exist.

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  8. Let f(x)={x+1,\ if\ x >0, and x-1,\ if\ x<0dot Prove that ("lim")(x->1...

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  9. Let f(x)=\ {x+5,\ if\ x >0 and x-4,\ if\ x<0 Prove that ("lim")(x->0)\...

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  10. Find ("lim")(x->3)\ f(x) \ where\ f(x)={4,\ if\ x >3 x+1, \ if\ x<3

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  11. Find lim(xrarr0)f(x)a n d(lim)(x-&gt;1)f(x),""""w h e r e""""f(x)=[2x+...

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  12. Find (lim)(x->1)f(x),""w h e r e""f(x)=[x^2-1, xlt=1-x^2-1, x >1

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  13. Evaluate ("lim")(x->0)f(x),\ w h e r e\ f(x)={(|x|)/x ,\ x!=0 , ...

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  14. Find ("lim")(x->1^+)1/(x-1)dot

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  15. Evaluate the following one sided limit: ("lim")(x->2^-)\ (x-3)/(x^2-4)

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  16. Evaluate the following one sided limit: lim(x->-8^+)(2x)/(x+8)

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  17. Evaluate the following one sided limit: ("lim")(x->pi//2^+)secx

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  18. Evaluate the following one sided limit: ("lim")(x->-pi//2^+)(2-cotx)

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  19. Evaluate the following one sided limit: ("lim")(x->2^+)(x-3)/(x^2-4)

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  20. Evaluate the following one sided limit: ("lim")(x->0^+)2/(x^(1//5))

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