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Evaluate the following limit: (lim)(thet...

Evaluate the following limit: `(lim)_(theta->0)(1-cos4theta)/(1-cos6theta)`

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`(lim)_(theta->0)(1-cos4theta)/(1-cos6theta)`

L'Hopital Rule:

`lim_(x rightarrow b) (f(x))/(g(x))=lim_(x rightarrow b) (f'(x))/(g'(x))`

`(lim)_(theta->0)(4sin4theta)/(6sin6theta)`

We know,

`(lim)_(x->0) (sin x)/(x)=1`

`(lim)_(theta->0)(4*4theta*1)/(6*6theta*1)`

`(lim)_(theta->0)(16theta)/(36theta)=4/9`

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Knowledge Check

  • lim_(thetato0)(1-cos4theta)/(1-cos6theta) is equal to

    A
    `4/9`
    B
    `1/2`
    C
    `-1/2`
    D
    `-1`

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