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Sketch the graph of an example of a rati...

Sketch the graph of an example of a rational function f that satisfies all the given conditions.
(i) `f(0)=0,f(1), lim_(xrarroo) f(x)=0,f " is odd"`
(ii) `lim_(xrarr0^(+)) f(x)=oo,lim_(xrarr0^(-)) f(x)=-oo,lim_(xrarroo) f(x)=1,lim_(xrarr-oo) f(x)=1`
(iii) `lim_(xrarr-2) f(x)=oo, lim_(xrarr-oo) f(x)=3,lim_(xrarroo) f(x) = 3 , f(0)=0`

Answer

Step by step text solution for Sketch the graph of an example of a rational function f that satisfies all the given conditions. (i) f(0)=0,f(1), lim_(xrarroo) f(x)=0,f " is odd" (ii) lim_(xrarr0^(+)) f(x)=oo,lim_(xrarr0^(-)) f(x)=-oo,lim_(xrarroo) f(x)=1,lim_(xrarr-oo) f(x)=1 (iii) lim_(xrarr-2) f(x)=oo, lim_(xrarr-oo) f(x)=3,lim_(xrarroo) f(x) = 3 , f(0)=0 by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

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Knowledge Check

  • lim_(xrarr0)(xe^x -sin2x)/x is :

    A
    2
    B
    0
    C
    `-1`
    D
    1

  • lim_(xrarr0)[xe^(2x) +tanx]/x is :

    A
    1
    B
    2
    C
    0
    D
    does not exist

  • If lim_(xto0)f(x)=l in R , then

    A
    `lim_(xto0)f(x^(2))=l^(2)`
    B
    `lim_(xto0)f((x)/(l))=1`
    C
    `lim_(xto0)f(2x)=2l`
    D
    `lim_(xto0)f(-x)=l`

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    Find (a) lim_(xrarr0)tanx/|x|

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