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Question
Evaluate the following limit.
`lim_(x -> 0) (sin ax + bx)/(ax + sin bx) a, b, a+ b != 0`
Solution
`lim_(x → 0)(sinax + bx)/(ax + sinbx)`
Dividing numerator and denominator by x
= `lim_(x → 0)((sin ax/x + b)/(a + sin bx/x))`
= `lim_(x → 0)(((sinax)/ax) a + b)/(a + ((sinbx)/bx) b)`
= `(1. a + b)/(a + 1.b)`
= `(a + b)/(a + b)`
= 1, a + b ≠ 0
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