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Solve lim(xrarr1)[sin^(-1)x] (where [.]...

Solve
`lim_(xrarr1)[sin^(-1)x]`
(where [.] denotes greatest integer function.)

Text Solution

Verified by Experts

Put `sin^(-1)x=t`
`therefore lim_(trarrpi/2)[t]implies[pi/2]=1implieslim_(trarrpi/2)[t]implies[pi/2]=1`
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PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Evaluate the right hand limit and left hand limit of the function f(x)...

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  2. Evaluate lim(xrarr1)(sqrt(1-cos2(x-1)))/(x-1)

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  3. Solve lim(xrarr1)[sin^(-1)x] (where [.] denotes greatest integer func...

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  4. Solve lim(xrarr0^+)[sinx/x] (where [.] denotes greatest integer funct...

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  5. Solve lim(xrarr0^-)[sinx/x] (where [.] denotes greatest integer funct...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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