lim x->0 sinbx/x
To find the limit of the function sin(bx)/x as x approaches 0, we can use L’Hôpital’s rule
To find the limit of the function sin(bx)/x as x approaches 0, we can use L’Hôpital’s rule. This rule states that if the limit of f(x)/g(x) as x approaches a is of the form 0/0 or ±∞/∞, where f(x) and g(x) are both differentiable functions, then the limit of f(x)/g(x) as x approaches a is equal to the limit of the derivative of f(x) divided by the derivative of g(x) as x approaches a.
In this case, the limit is of the form 0/0 as x approaches 0. So, let’s apply L’Hôpital’s rule:
lim x->0 (sin(bx)/x) = lim x->0 (b*cos(bx)/1) = b*cos(0)/1 = b
Therefore, the limit of sin(bx)/x as x approaches 0 is equal to b.
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