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

`lim_(x->pi)((sin3x-3sinx)/((pi-x)^3))`

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Verified by Experts

The correct Answer is:
`-1`
Given limit `=lim_(xto pi)((3sinx-4sin^(3)x-3sinx))/((pi-x)^(3))`
`=lim_(xto pi)(-4sinx)/((pi-x)^(3))=lim_(thetato0)(-4sin^(3)(pi+theta))/((-theta)^(3))where (x-pi)=theta`
`=-4lim_(thetato0)((sintheta)/(theta))=(-4xx1)=-4.`
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RS AGGARWAL-LIMIT-EXERCISE 27B
  1. Evaluate the following limits: lim(xrarr(pi)/(4))((cosec^(2)x-2))/((...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. Evaluate the following limits: lim(xrarr0)((e^(tan-x)-1))/(tanx)

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  16. Evaluate the following limits: lim(xrarr0)((e^(3+x)-sinx-e^(3)))/(x)

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  17. Evaluate the following limits: lim(xrarr0)((e^(tanx)-1))/(tanx)

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  18. Evaluate the following limits: lim(xrarr0)((e^(tanx)-1))/(x)

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

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  20. Evaluate the following limits: lim(xrarr0)(sinax+bx)/(ax+sinbx),wher...

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