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If f(x) is defined as f(x)={{:(x,0l...

If f(x) is defined as
`f(x)={{:(x,0lexlt(1)/(2)),(0,x=(1)/(2)),(1-x,(1)/(2)ltxle1):}`
then evaluate : `lim_(xrarr(1)/(2)) f(x)`

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NAGEEN PRAKASHAN ENGLISH-LIMITS AND DERIVATIVES-EX-13A
  1. lim(xrarr1) [(x-2)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+2x)]

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  2. (i) lim(xrarra) (x^(m)-a^(m))/(x^(n)-a^(n)) (ii) lim(xrarra) ((1+x)^...

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  3. lim(xrarroo) (x^(3)+3x^(2)+6x+5)/(x^(3)+x+2)

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  4. lim(x to 0) ((2x-3)(3x-4))/((4x-5)(5x -6))

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  5. lim(xrarroo) (1^(2)+2^(2)+3^(2)+....+x^(2))/(x^3)

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  6. lim(xrarroo) (2x)/(1+4x)

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  7. underset(xrarroo)(1^(2)+2^(2)+3^(2)+...+x^(2))/(X^(3))

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  8. lim(x to oo ) (sqrt(3x^(2)-1)-sqrt(2x^(2)-3))/(4x+3)

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  9. Evaluate : lim(x to oo) sqrt(x^(2)+x +1) - sqrt(x^(2)+1)

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  10. lim(xrarrpi) (sin(pi-x))/(pi(pi-x))

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  11. (i) lim(xrarrpi) (cos ecx-cotx)/(x) (ii) lim(xrarr0) (sinx-2sin3x+si...

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  12. (i) lim(x to 0) (x tan 4x)/(1-cos 4x) (ii) lim(y to 0) ((x+y)sec(x...

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  13. Lim(x to pi/2) (1+cos 2x)/(pi-2x)^(2)

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  14. If f(x) is defined as follows: f(x)={{:(1,x,gt0),(-1,x,lt0),(0,x,=0)...

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  15. If f(x) is defined as f(x)={{:(x,0lexlt(1)/(2)),(0,x=(1)/(2)),(1-...

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  16. If f(x) is defined as f(x)={{:(2x+3,x,le 0),(3x+3,x,ge 0):} then...

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  17. If f(x)=(|x|)/(x), then show that lim(xrarr0) f(x) does not exist.

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  18. If f(x)=(|x-a|)/(x-a), then show that lim(xrarra) f(x) does not exist...

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  19. If f(x) is defined as f(x)={{:(x,0le,xle1),(1,x,=1),(2-x,x,gt1):} ...

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  20. If f(x)={{:(a+bx,xlt1),(4,x=1),(b-ax,xgt1):} and underset(xrarr1)f(x...

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