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Evaluate the following limits: lim(xra...

Evaluate the following limits:
`lim_(xrarr0)(ax+x cosx)/(b sinx)`

Text Solution

Verified by Experts

The correct Answer is:
(a+1)/(b)`
`lim_(xto0)(ax+xcosx)/(bsinx)=lim_(xto0)(a+cosx)/(b((sinx)/(x)))" "["dividing num. and denom. by x"]`
`=((a+1))/((bxx1))=((a+1))/(b).`
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RS AGGARWAL-LIMIT-EXERCISE 27B
  1. Evaluate the following limits: lim(xrarr0)((e^(tanx)-1))/(tanx)

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

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

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

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  5. lim(x->pi)(sin(pi-x)/(pi(pi-x)))

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  6. lim(x->pi/2) (tan 2x)/(x-pi/2)

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  7. Evaluate the following limits: lim(xrarr0)(cos2x-1)/(cosx-1)

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  8. Evaluate the following limits: lim(xrarr0)(cosec x-cotx)

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  9. Evaluate the following limits: lim(xrarr0)(1-cos2mx)/(1-cos2nx)

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

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  11. Evaluate the following limits: lim(xrarr0)(sin^(2)mx)/(sin^(2)nx)

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

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  13. The value of lim(x->0)(sec4x-sec2x)/(sec3x-secx) is

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  14. Evaluate the following limits: lim(x to0)(sqrt2-sqrt(1+cosx))/(2x+si...

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  15. Evaluate the following limits: lim(xrarr0)(sqrt(1+sinx)-1sqrt(1-sinx...

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  16. lim(x->pi/6)(2-sqrt(3)cosx-sinx)/((6x-pi)^2)

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  17. Evaluate the following limits: lim(xrarr0)(cos ax-cos bx)/(cos cx-1)

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  18. Evaluate the following limits: lim(xrarra)(cosx-cosa)/(cotx-cota)

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  19. lim(x rarr pi/4)(tan^3x-tanx)/(cos(x+pi/4)

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  20. Evaluate the following limits: lim(xrarr(pi)/(2))(sqrt2-sqrt(1+sinx)...

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