lim x->0 sinbx/x
To evaluate the limit as x approaches 0 of sin(bx)/x, where b is a constant, we can use L’Hôpital’s Rule
To evaluate the limit as x approaches 0 of sin(bx)/x, where b is a constant, we can use L’Hôpital’s Rule.
Applying L’Hôpital’s Rule, take the derivative of the numerator and denominator separately. The derivative of sin(bx) with respect to x is b*cos(bx), and the derivative of x with respect to x is 1.
Therefore, the limit becomes:
lim x->0 (b*cos(bx))/1
Now, we can substitute x = 0 into the expression:
lim x->0 (b*cos(0))/1
cos(0) is equal to 1, so the expression simplifies to:
lim x->0 b/1
Since x is approaching 0, we can ignore it in the limit. Thus, the final limit is:
b
Therefore, lim x->0 sin(bx)/x = b.
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