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Let the function be
f ( x ) = sin a x sin b x
We have to find the value of the function at Limit x → 0
At a particular point at x = 0 , the function takes the form of 0 0 .
We need to simplify the term to remove 0 0 form.
According to the trigonometric theorem,
lim x → 0 sin x x = 1 (1)
lim x → 0 sin a x sin b x = lim x → 0 sin a x lim x → 0 sin b x (Applying limits to num and den)
On solving numerator and denominator separately we get,
lim x → 0 sin a x a x ⋅ a x lim x → 0 sin b x b x ⋅ b x
As x → 0 so a x → 0 , b x → 0 thus from equation 1
f ( x ) = lim a x → 0 sin a x a x ⋅ a x lim b x → 0 sin b x b x ⋅ b x = 1 ( a x ) 1 ( b x ) = a b
Thus the value of the given expression lim x → 0 sin a x sin b x = a b
Let the function be
We have to find the value of the function at Limit
At a particular point at
We need to simplify the term to remove
According to the trigonometric theorem,
On solving numerator and denominator separately we get,
As
Thus the value of the given expression
