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Evaluate the following limits: lim(xra...

Evaluate the following limits:
`lim_(xrarr0)((sin2x+3x))/((2x+sin3x))`

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The correct Answer is:
1
Given limit `=(2x(lim_(xto0)(sin2x)/(2x))+3)/(2+(lim_(xto0)(sin3x)/(3x)))=((2xx1+3))/(2+(3xx1))=5/5=1.`
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RS AGGARWAL-LIMIT-EXERCISE 27B
  1. Evaluate the following limits: lim(xrarr0)((sinx-2sin3x+sin5x))/(x)

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  2. Evaluate the following limits: lim(xrarr pi//6)((2sin^(2)x+sinx-1))/...

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  3. Evaluate the following limits: lim(xrarr0)((sin2x+3x))/((2x+sin3x))

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  4. Evaluate the following limits: lim(xrarr0)((tan2x-x))/((3x-tanx))

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

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  6. Evaluate the following limits: lim(xrarr0)((xcosx+sinx))/((x^(2)+tanx...

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  7. Evaluate the following limits: lim(xrarr0)((tanx-sinx))/(sin^(3)x)

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  8. Evaluate the following limits: lim(xrarr0)(xcosecx)

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  9. Evaluate the following limits: lim(xrarr0)(x cot2x)

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  10. Evaluate the following limits: lim(xrarr0)(sinxcosx0)/(3x)

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  11. Evaluate the following limits: lim(xrarr0)(sin(x//4))/(x)

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  12. Evaluate the following limits: lim(xrarr0)(tan(x//2))/(3x)

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  13. Evaluate the following limits: lim(xrarr0)((1-cosx))/(sin^(2)x)

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  14. Evaluate the following limits: lim(xrarr0)((1-cos3x))/(x^(2))

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  15. Evaluate the following limits: lim(xrarr0)((1-cos2x))/(sin^(2)2x)

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  16. Evaluate the following limits: lim((1-cos2x))/(3tan^(2)x)

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  17. Evaluate the following limits: lim(xrarr0)((1-cos2x))/((1-cos6x))

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  18. Evaluate, underset(xrarr0)"lim"(1-cosmx)/(1-cosnx)

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  19. Evaluate underset(xrarr0)"lim"(2sinx-sin2x)/(x^(3))

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  20. Evaluate the following limits: lim(xrarr0)((tanx-sinx))/(sin^(3)x)

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