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Evaluate the following limit: underset( ...

Evaluate the following limit: `underset( x rarr 1) ( "lim")(1+(x-1)^2)/(1+x^2)`

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Given,
`(lim)_(x->1)(1+(x−1)^2)/(1+x^2)`
`=(lim)_(x->1)(1+(1−1)^2)/(1+1^2)`
`=1/2`
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RD SHARMA-LIMITS-All Questions
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  2. Evaluate the following limit: underset( x rarr 3) ( "lim")(sqrt(2x+3))...

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  3. Evaluate the following limit: underset( x rarr 1) ( "lim")(1+(x-1)^2)/...

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  4. Evaluate the following limit: underset( x rarr 2) ( "lim")(3-x)

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  5. Evaluate the following limit: underset( x rarr 0) ( "lim")(3x+1)/(x+3)

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  6. Evaluate:underset( x rarr 2) ( "lim")(x^3-6x^2+11 x-6)/(x^2-6x+8)

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  7. Evaluate : underset( x rarr 1) ( "lim")(2/(1-x^2)+1/(x-1))

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  8. Evaluate:underset( x rarr sqrt(2)) ( "lim")(x^9-3x^8+x^6-9x^4-4x^2-16 ...

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  9. Evaluate the following limit: lim(x rarr -5)(2x^2+9x-5)/(x+5)

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  10. Evaluate the following limit: underset( x rarr 3) ( "lim")(x^4-81)/(x^...

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  11. Evaluate the following limit: underset( x rarr - 1/2) ( "lim")(8x^3+1)...

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  12. Evaluate the following limit: underset( x rarr 2) ( "lim")(x^4-16)/(x-...

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  13. Evaluate the following limit: underset( x rarr sqrt(2)) ( "lim")(x^2-2...

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  14. Evaluate the following limit: underset( x rarr sqrt(3)) ( "lim")(x^4-9...

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  15. Evaluate the following limit: underset( x rarr 1) ( "lim")(1/(x^2+x-2)...

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  16. Evaluate the following limit: underset( x rarr 2) ( "lim")(1/(x-2)-2/(...

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  17. Evaluate the following limit: underset( x rarr 2) ( "lim")(1/(x-2)-4/(...

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  18. lim(x->1) ((x^4-3x^2+2)/(x^3-5x^2+3x+1))

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  19. Evaluate the following limit: underset( x rarr - 2) ( "lim")(x^3+x^2+4...

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  20. Evaluate the following limit: underset( x rarr 3) ( "lim")(x^2-4x+3)/...

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