The limit equals the ratio of the derivatives at x=0. That is called L'Hopital's rule.
Limit (12 cos 4x) / (3 cos x)
@ x=4 = ?
find limit :
lim (3sin4x / sin3x )
x--> 0
4 answers
sorry, I don't understand can you explain it, please ?
If you do not understand derivatives, then you will have to find the trig equivalent of the multiangle (identies)equivalents, and reduce the fractions.
The limit is of the form:
Lim x--> 0 f(x)/g(x)
where f(0) = g(0) = 0. So we can't take the limits for f and g separately and divide them.
Rewrite the limit as:
Lim x--> 0 [f(x) - 0]/[g(x) - 0] =
Lim x--> 0 [f(x)-f(0)]/[g(x)-g(0)]
Lim x-->0{[f(x)-f(0)]/x}/{[g(x)-g(0)]/x}
The limits of the numerator and denominator are the derivatives at zero. If they both exist and are nonzero then the limit is the ratio of these derivatives.
Lim x--> 0 f(x)/g(x)
where f(0) = g(0) = 0. So we can't take the limits for f and g separately and divide them.
Rewrite the limit as:
Lim x--> 0 [f(x) - 0]/[g(x) - 0] =
Lim x--> 0 [f(x)-f(0)]/[g(x)-g(0)]
Lim x-->0{[f(x)-f(0)]/x}/{[g(x)-g(0)]/x}
The limits of the numerator and denominator are the derivatives at zero. If they both exist and are nonzero then the limit is the ratio of these derivatives.
0 answers