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lim(x->0)(sin3x+7x)/(4x+sin2x)...

`lim_(x->0)(sin3x+7x)/(4x+sin2x)`

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`lim_(xto0)((sin3x+7x)/(4x+sin2x))=lim_(xto0)(((sin3x)/(x)+7)/(4+(sin2x)/(x))) " "["dividing num. and denom. by x"]`
`=lim_(xto0){((sin3x)/(3x).3+7)/(4+((sin2x)/(2x)).2)}=([3xxlim_(3xto0)(sin3x)/(3x)]+7)/(4+[2xxlim_(2xto0)((sin2x)/(2x))])`
`=((3xx1)+7)/(4+(2xx1))=10/6=5/3.`
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RS AGGARWAL-LIMIT-SOLVED EXAMPLES
  1. Evaluate: (i) lim(xrarr0)((tanx-sinx)/sin^(3)x)" "(ii)lim(xrarr0)...

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  2. Evaluate lim(xrarr0)((x^(3)cotx)/(1-cosx)).

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  3. lim(x->0)(sin3x+7x)/(4x+sin2x)

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  4. Evaluate lim(x-> 0) (tan3x-2x)/(3x- sin^2 x)

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  5. Evaluate lim(xrarr0)(xtan4x)/(1-cos4x).

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  6. Evaluate lim(xrarr0)((1-cosxsqrt(cos2x)))/(x^(2)).

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  7. Evaluate lim(xrarr(pi)/(4))((sinx-cosx))/((x-(pi)/(4))).

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  8. Evaluate lim(xrarr(pi)/(2))(cosx)/(((pi)/(2)-x)).

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  9. Evaluate lim(xrarr(pi)/(6))((sqrt3sinx-cosx))/((x-(pi)/(6))).

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  10. Let f(x){:{(2x+3",",xle0),(3(x+1)",",xgt0.):} Find (i) lim(xrarr0)f(...

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  11. Let f(x)={:{(x^(2)-1",",xle1),(-x^(2)-1",",xgt1.):} "Find"lim(xrarr1)f...

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  12. Let f(x)={:{((|x|)/(x)",",xne0),(0",",x=0.):} Find lim(xrarr0)f(x).

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  13. Suppose f(x)={(a+bx, x<1), (4, x=1), (b-ax, x>1):} and if lim(xrarr1) ...

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

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

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  16. Let a(1),a(2),...,a(n) be fixed real numbers and let f(x)=(x-a(1))(...

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  17. Let f(x)={x}= greater integer less than or eqal to x. For any integer ...

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  18. If is an odd function and underset(xto0)f(x) exists then prove tha...

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  19. If f is an even function, prove that lim(xto0^(-)) (x)=lim(xto0^(+)) ...

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  20. Show that lim(xto0^(-)) ((e^(1//x)-1)/(e^(1//x)+1)) does not exist.

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