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If f(x)={(absx + 1 , x lt 0),(0 , x = 0)...

If f(x)=`{(absx + 1 , x lt 0),(0 , x = 0),(absx - 1 , x gt 0) :}` , for what value(s) of a does `lim_(x rarr 0)` f(x) exist ?

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A N EXCEL PUBLICATION-LIMITS AND DERIVATIVES-QUESTION BANK
  1. Evaluate lim(x rarr 5) f(x) , where f(x) =absx - 5

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  2. Suppose f(x) ={ (a+bx , x lt 1),(4 , x = 1), (b - ax , x gt 1) :} and ...

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  3. If f(x)={(absx + 1 , x lt 0),(0 , x = 0),(absx - 1 , x gt 0) :} , for ...

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  4. If fthe function f(x) satisfies lim(x rarr 1) (f(x) - 2)/(x^2 - 1) = p...

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

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  6. Factorise x^3 - 6x^2 + 11x - 6 into two factors so that one factor is ...

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  7. Factorise x^2 - 6x + 8 into linear factors.

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  8. What is the rationalising factor of sqrt(1 + x) - sqrt(1 - x)?

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  9. Evaluate lim(x rarr 0) (sqrt(1 +x) - sqrt(1 - x))/(2x)

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  10. Evaluate lim(x rarr 0) (x^10 - 1024)/(x - 2)

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  11. lim(x rarr 2) (x^5 - 32)/(x - 2)

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  12. Evaluate lim(x rarr 2) (x^10 - 1024)/(x^5 - 32)

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  13. Factorise x^2 - 4

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  14. Rationalise sqrt(3x-2) - sqrt(x+2)

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  15. Evaluate lim(x rarr 2) (x^3 - 4)/(sqrt(3x -2) - sqrt(x+2))

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  16. Evaluate lim(x rarr -a) (x^9 + a^9)/(x+a)

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  17. Find the value of a if lim(x rarr -a) (x^9 + a^9)/(x + a) = 9

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  18. What is the value of (lim(x rarr 1) (x^n - 1)/( x - 1) for any integer...

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  19. Evaluate lim(x rarr 1) ((x + x^2 + .........+ x^n)-n)/(x - 1)

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  20. Given that lim(theta rarr 0) (sin theta)/theta = 1 and lim(theta rarr ...

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