lim x->0 sinbx/x
b
To find the limit of sinbx/x as x approaches 0, we can use L’Hopital’s Rule, which states that the limit of a quotient of two functions is equal to the limit of the derivative of the numerator divided by the derivative of the denominator, provided that the limit of the denominator is not zero and the derivatives exist.
Let’s apply this rule to the given function:
lim x->0 sinbx/x
We can differentiate both the numerator and denominator of the function with respect to x to get:
lim x->0 bcosbx/1
Now, we can evaluate the limit as x approaches zero:
lim x->0 bcosbx/1 = bcos(0)/1 = b
Therefore, the limit of sinbx/x as x approaches 0 is equal to b, where b is a constant.
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