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Evaluate lim(x rarr 0) (cos 2x - 1)/(cos...

Evaluate `lim_(x rarr 0) (cos 2x - 1)/(cos x - 1)`

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A N EXCEL PUBLICATION-LIMITS AND DERIVATIVES-QUESTION BANK
  1. Evaluate lim(x rarr pi) (sin (pi - x))/(pi(pi - x))

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  2. Evaluate lim(x rarr 0) (cos x)/(pi - x)

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  3. Evaluate lim(x rarr 0) (cos 2x - 1)/(cos x - 1)

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  4. Evaluate lim(x rarr 0) (ax + x cos x)/(b sin x)

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  5. Evaluate lim(x rarr 0) xsec x

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  6. Evaluate lim(x rarr 0) (sin ax + bx)/(ax + sin bx)

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  7. Evaluate lim(x rarr 0) (cosec x - cot x)

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  8. Evaluate lim(x rarr pi/2) (tan 2x)/(x - pi/2)

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  9. Evaluate lim(x rarr 0) f(x) and lim(x rarr 1) f(x), where f(x) = { (2x...

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  10. Evaluate lim(x rarr 1) where f(x) = {(x^2 - 1, x le 1),( -x^2 - 1 , x ...

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  11. Evaluate lim(x rarr 0)f(x), where f(x) ={ (absx/x , x ne 0), (0, x=0) ...

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  12. Evaluate lim(xrarr0) where f(x) ={(x/absx , x ne 0), (0 , x=0) :}

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  13. Evaluate lim(x rarr 5) f(x) , where f(x) =absx - 5

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

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

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

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

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

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

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