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Question
Evaluate the following limit.
`lim_(x -> 0) (ax + xcos x)/(b sin x)`
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Solution
`lim_(x → 0)(ax + xcosx)/(bsinx)`
= `lim_(x → 0) (x (a + cosx))/((sin x). b)`
= `lim_(x → 0)(x/(sinx)). (a + cosx)/b`
= `lim_(x → 0) (a + cosx)/b` .......`[∵ lim_(x → 0) x/(sinx) = 1]`
= `(a + cos 0)/b`
= `(a + 1)/b`
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