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Question
Evaluate the following limit.
`lim_(x -> 0) (sin ax)/ (bx)`
Solution
`lim_(x -> 0) (sin ax)/ (bx)`
At x = 0, the value of the given function takes the form `0/0`.
Now, `lim_(x → 0) (sin ax)/(bx)`= `lim_(x → 0) (sin ax)/(ax) xx (ax)/(bx)`
= `lim_(x → 0) ((sin ax)/(ax)) xx (a/b)`
= `a/blim_(ax → 0) ((sin ax)/(ax))` [x → 0 ⇒ ax → 0]
= `a/b xx 1` `[lim_(y->0) sin y/y = 1]`
= `a/b`
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