lim as x->0 of sinax/x
a
To evaluate this limit, we can use L’Hopital’s rule or the squeeze theorem.
Using L’Hopital’s rule:
lim as x->0 of sinax/x
= lim as x->0 of a*cos(ax)/1
= a*cos(0)/1
= a
Therefore, the limit as x approaches 0 of sin(ax)/x is equal to ‘a’.
Using the squeeze theorem:
We know that -1 <= sin(ax)/x <= 1 for all values of x (except x=0). Multiplying both sides by 'a', we get: -a <= a*sin(ax)/x <= a Using the squeeze theorem, we can say that as x approaches zero, the limit of a*sin(ax)/x is equal to 'a'. Therefore, the limit as x approaches 0 of sin(ax)/x is equal to 'a'.
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