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lim(xrarr0)("cosec"x-cotx)/(x) is equal ...

`lim_(xrarr0)("cosec"x-cotx)/(x)` is equal to

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Verified by Experts

The correct Answer is:
`1/2`
Given limit `lim_(xto0)((1-cosx))/(xsinx)=lim_(xto0)(2sin^(2)(x//2))/(2xsin(x//2)cos(x//2))=lim_(xto0)(tan(x//2))/(((x)/(2)))xx1/2=1/2.`
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RS AGGARWAL-LIMIT-EXERCISE 27B
  1. Evaluate the following limits: lim(xrarr0)((tanx-sinx))/(sin^(3)x)

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  2. Evaluate the following limits: lim(xrarr0)((tan2x-sin2x))/(x^(3))

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  3. lim(xrarr0)("cosec"x-cotx)/(x) is equal to

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  4. Evaluate the following limits: lim(xrarr0)((cot2x-cosecex))/(x)

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  5. Evaluate the following limits: lim(xrarr0)((cosecx-cotx))/(x^(3))

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  6. lim(xrarr(pi//4))(sec^(x)-2)/(tanx-1) is

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  7. Evaluate the following limits: lim(xrarr(pi)/(4))((cosec^(2)x-2))/((...

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  8. Evaluate the following limits: lim(xrarr (pi)/(4))(tanx-1)/((x-(pi)/(...

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  9. lim(x->pi)((sin3x-3sinx)/((pi-x)^3))

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  10. Evaluate: ("lim")(xvecpi/2)(1+cos2x)/((pi-2x)^2)

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  11. Evaluate the following limits: lim(xrarra)((sinx-sina))/((x-a))

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  12. Evaluate the following limits: lim(xrarra)((sinx-sina))/((x-a))

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  13. Evaluate the following limits: lim(xrarra)((sinx-sina))/((sqrtx-sqrta...

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  14. Evaluate the following limits: lim(xrarr0)((sin5x-sin3x))/(sinx)

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  15. Evaluate the following limits: lim(xrarr0)((cos3x-cos5x))/(x^(2))

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  16. Evaluate the following limits: lim(xrarr0)((sin3x+sin5x))/((sin6x-si...

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  17. Evaluate the following limits: lim(xrarr0)([sin(2+x)-sin(2-x)])/(x)

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  18. Evaluate the following limits: lim(xrarr0)((1-cos2x))/((cos2x-cos8x)...

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  19. Evaluate the following limits: lim(xrarr(pi)/(2))((pi)/(2)-x)tanx

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  20. Evaluate the following limits: lim(xrarr0)((sqrt(1+2x)-sqrt(1-2x)))/...

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