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Find the value of 'a' such that lim(x ra...

Find the value of 'a' such that `lim_(x rarr 2)` f(x) exists, where
`f(x) = {(ax+5, x lt 2),(x-1, x ge 2):}`

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`lim_(x rarr 0) f(x)` exists if m = n , `lim_(x rarr 1)` f(x) exists for any integral value m,n
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MAHAVEER PUBLICATION-LIMITS-QUESTION BANK
  1. Evaluate the following limits : lim(x rarr 1) (3x + 1) (x+ 1)

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  2. Evaluate the following limits : lim(x rarr -1) (x+1)/(x+2)

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  3. Evaluate the following limits : lim(x rarr 0) (px + q)/(ax + b)

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  4. underset(xrarr-2)"lim"((1)/(x)+(1)/(2))/(x+2)

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  5. Evaluate the following limits: lim(xto-2)((x^(2)-25)/(x-5))

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  6. Evaluate the following limits : lim(x rarr 1/3) (9x^2-1)/(3x-1)

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  7. Evaluate the following limits : lim(x rarr 2) (x^2-x-2)/ (x^2-3x+2)

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  8. Evaluate the following limits : lim(x rarr 1) [1/(x-1)-2/(x^2-1)]

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  9. Evaluate the following limits : lim(x rarr 2) (sqrt(3x-2) -x)/(2-sqr...

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  10. Evaluate the following limits : lim(x rarr 0) x/(5-|x|)

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  11. Evaluate the following limits : lim(x rarr -2) (x^11-1)/(x^7 -1)

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  12. (lim)(x->0)(cosx)/(pi-x)

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  13. (lim)(x->0)(cos2x-1)/(cosx-1)

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  14. lim(x->0)(sina x+b x)/(a x+sinb x)

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  15. underset(xrarr0)"lim"(cos ec x -cot x)

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  16. Evaluate the following limits : lim(x rarr 1) (x^(1/20)-1)/(x^(1/40)...

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  17. underset(xrarr0)"lim"(sinax)/(sinbx),a,bne0

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  18. Show that lim(x rarr 5) (|x -5|)/(x-5) does not exists.

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  19. Find the value of 'a' such that lim(x rarr 2) f(x) exists, where f(x...

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  20. If f(x)={{:(mx^(2)+n",", x lt 0), (nx+m",", 0 le x le 1), (nx^(3)+m",...

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