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Solve lim(xrarr0^-)[tanx/x] (where [.] d...

Solve
`lim_(xrarr0^-)[tanx/x]`
(where [.] denotes greatest integer function.)

Text Solution

Verified by Experts

Here, `lim_(x rarr 0^-)[tanx/x]`
Put `tanx/x=timpliestrarr1^+` as `xrarr0^-`{i.e., as `xrarr0-h`
`implies t rarr1+h}`
`therefore lim_(trarr1^+)[t]=[1+h]=1`
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PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Solve lim(xrarr0^-)[sinx/x] (where [.] denotes greatest integer funct...

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  2. Solve lim(xrarr0^+)[tanx/x] (where [.] denotes greatest integer functi...

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  3. Solve lim(xrarr0^-)[tanx/x] (where [.] denotes greatest integer functi...

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  4. Evaluate lim(xrarr1)(x^(P+1)-(P+1)x+P)/((x+1)^2)

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  5. Evaluate lim(xrarr0) tan(2x )/x

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  6. Evaluate lim(xrarra)(2-a/x)^("tan"(pix)/(2a))

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  7. The graph of function y=f(x) has a unique tangent at (e^a,0), through ...

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  8. Evaluate lim(nrarrinfty)([x]+[2x]+[3x]+......+[nx])/(n^2) where [.] d...

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  9. Evaluate lim(xrarr0)(int0^(x^2) costdt)/(xsinx)

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  10. Evaluate lim(xrarr0)(x-int0^(x) cost^2dt)/(x^3-6x)

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  11. Evaluate : lim(x to 0) {tan(pi/4+x)}^(1/x)

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  12. If alpha and beta be the roots of the quadratic equation ax^2+bx+c=0 t...

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  13. Let a=min{x^2+2x+3, x in R} and b=lim(thetararr0)(1-costheta)/(theta^2...

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  14. If f(x)={(2x+3, "when x" lt 0),(0, "when x"=0),(x^2+3, "when x"gt 0):}...

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  15. Let y=f(x) be defined parametrically as y=t^2+t|t|, x=2t-|t|, t in R, ...

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  16. Let f(x) be a continuous function defined for 1 le x le 3. If f(x) tak...

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  17. Find the points points of discontinuity of y=1/(u^2+u-2) where u=1/(x-...

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  18. If f(x)=[x], where [.] denotes greatest integer function. Then check t...

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  19. Let f(x)={({1+|sinx|}^(a//|sinx|), -pi//6ltxlt0),(b, x=0),(e^(tan2x...

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  20. Discuss the continuity of f(x)=[tan^(-1)x]

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