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(i) lim(xrarra) (x^(m)-a^(m))/(x^(n)-a^(...

(i) `lim_(xrarra) (x^(m)-a^(m))/(x^(n)-a^(n))`
(ii) `lim_(xrarra) ((1+x)^(1//n)-1)/(x)`

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lim_(x rarr0)((1-x)^(n)-1)/(x)

Evaluate lim_(xrarra)((x^(m)-a^(m))/(x^(n)-a^(n))).

lim_(x to a) (x^(m)-a^(m))/(x^(n)-a^(n)) is equal to

lim_(x rarr0)((x+1)^(n)-1)/(x)

lim_(x rarr0)((x+1)^(n)-1)/(x)

lim_(xrarr1)(x^(m)-1)/(x^(n)-1) is equal to

lim_(x rarr a)(x^(m)-a^(m))/(x^(n)-a^(n))=((m)/(n))a^(m-n) if m>n

Evaluate: lim_(x rarr a) [(x^(n)-a^(n))/(x^(m)-a^(m))] .

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NAGEEN PRAKASHAN-LIMITS AND DERIVATIVES-EX-13A
  1. lim(xrarr0) (sin ax+bx)/(ax+sin bx),ane0,bne0,a+bne 0

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  2. lim(xrarr1) [(x-2)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+2x)]

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

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

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

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  6. lim(xrarroo) (1^(2)+2^(2)+3^(2)+....+x^(2))/(4x+3)

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

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

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

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  10. (i) lim(xrarroo) "(sqrt(x^(2)+x+1)-sqrt(x^(2)+1)) (ii) lim(nrarroo)...

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

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

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

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  14. (i) lim(x to (pi)/(2)) (1+cos 2x)/((pi-2x)^(2)) (ii) lim( x to 0) (1...

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

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

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  17. If f(x) is defined as f(x)={{:(2x,+,3,x,le 0),(3x,+,3,x,le0):} t...

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

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

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  20. If f(x) is defined as f(x)={{:(x,0le,xle1),(2,x,=1),(20x,x,gt1):} ...

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