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Let a(1), a(2),…,a(n) be fixed real numb...

Let `a_(1), a_(2),…,a_(n)` be fixed real numbers and define a function `f(x)=(x-a_(1))(x-a_(2))…(x-a_(n)).`
What is `lim_(xrarra_(1))f(x)` ? For some `a ne a_(1), a_(2), …..,a_(n)`, compute `lim_(xrarra)(f(x)`.

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The correct Answer is:
`lim_(xrarra_(1))f(x)` exists for all `ane 0`.
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NCERT TAMIL-LIMITS AND DERIVATIVES-EXERCISE 13.1
  1. Evaluate the following limits in lim(xrarr0)(sinax)/(bx)

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  2. Evaluate the following limits in lim(xrarr0)(sinax)/(sinbx),a,b ne0

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  3. Evaluate the following limits in lim(xrarrpi)(sin(pi-x))/(pi(pi-x))

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  4. Evaluate the following limits in lim(xrarr0)(cosx)/(pi-x)

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  5. Evaluate the following limits in lim(xrarr0)(cos2x-1)/(cosx-1)

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  6. Evaluate the following limits in lim(xrarr0)(ax+x cosx)/(b sinx)

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  7. Evaluate the following limits in lim(xrarr0)x secx

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  8. Evaluate lim(xto0)(sinax+bx)/(ax+sinbx)a,b,a+bne0.

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  9. Evaluate the following limits in lim(xrarr0)("cosec "x-cotx)

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  10. Evaluate lim(xto(pi)/(2))(tan2x)/(x-(pi)/(2))

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  11. Find lim(xto0)f(x) and lim(xto1)f(x), where f(x)={{:(2x+3","xle0),(3(x...

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  12. Find lim(xto1)f(x), where f(x)={{:(x^(2)-1","xle1),(-x^(2)-1","xgt1):}

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  13. Evaluate lim(xto0)f(x), where f(x)={{:((|x|)/(x)","xne0),(0","x=0):}

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  14. Find lim(xto0)f(x), where f(x)={{:((x)/(|x|)","xne0),(0","x=0):}

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  15. Find lim(xto5)f(x), where f(x)=|x|-5

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

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  17. Let a(1), a(2),…,a(n) be fixed real numbers and define a function f(x)...

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  18. If f(x)={{:(|x|+1","xlt0),(0","x=0),(|x|-1","xgt0):} For what value (s...

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  19. If the function f(x) satisfies lim(xrarr1)(f(x)-2)/(x^(2)-1)=pi, evalu...

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  20. If f(x)={{:(mx^(2)+n","xlt0),(nx+m","0lexle1),(nx^(3)+m","xgt1):} Fo...

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