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Question
Evaluate: `lim_(x -> 0) (sin 3x)/(sin 7x)`
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Solution
Given that `lim_(x -> 0) (sin 3x)/(sin 7x)`
= `lim_(x -> 0) ((sin 3x)/(3x) xx 3x)/((sin 7x)/(7x) xx 7x)`
= `(lim_(3x -> 0) ((sin 3x)/(3x)))/(lim_(7x -> 0) ((sin 7x)/(7x))) xx 3/7`
= `1/1 xx 3/7`
= `3/7` ......`[because lim_(x -> 0) sinx/x = 1]`
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