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Prove that the function defined by f(x) ...

Prove that the function defined by `f(x) = t a n x`is a continuous function.

Text Solution

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Let `f(x)=tanx`
`f(x)=sinx/cosx` is defined for all real number except cosx=0
`=>x=(2n+1)pi/2`
Let p(x)=sinx and q(x)=cosx
...
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Knowledge Check

  • If f(x) is continuous function , then

    A
    ` int_9^16 f(x)dx = 7f(c)` for some 'c' lying between 9 and 16
    B
    ` int_9^16 f(x)dx` = ` int_tan9^tan16 (f(tan^(-1) t))/(1+ t^(2))dt`
    C
    ` int_9^16 f(x)dx = (tan16 -tan9)f(tan^(-1)c)/(1+c^(2))` for some 'c' lying between tan9 and tan16
    D
    none of these

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