lim x->0 sinbx/x
To find the limit as x approaches 0 of sin(bx)/x, where b is a constant, we can use L’Hospital’s Rule if the limit is in an indeterminate form of 0/0
To find the limit as x approaches 0 of sin(bx)/x, where b is a constant, we can use L’Hospital’s Rule if the limit is in an indeterminate form of 0/0.
First, write the limit as:
lim x->0 (sin(bx))/(bx)
Now, if we take the derivative of both the numerator and denominator with respect to x, we have:
lim x->0 (b*cos(bx))/(b)
Since b is a constant, its derivative is 0. So, the limit expression simplifies to:
lim x->0 cos(bx)
Now, evaluate this limit as x approaches 0:
lim x->0 cos(bx) = cos(0) = 1
Therefore, the limit of sin(bx)/x as x approaches 0 is 1.
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