lim (sin 4x/3x)
x->0
Is the answer 4/3 or -3/4?
as x -->0 sin 4x --> 4x
x/x is even and always +
so
4/3
thank you!
To find the limit of the given expression, we can apply the special limit property in calculus known as the "Sine of X over X" limit. This limit states that as x approaches 0, the limit of sin(x)/x is equal to 1.
Using this property, let's rewrite the given expression in terms of sin(x)/x:
lim (sin 4x/3x) = lim (4/3) * (sin 4x)/(4x)
By simplifying the expression, it becomes:
lim (sin 4x)/3x = (4/3) * lim (sin 4x)/(4x)
Now, since we know that the limit of sin(x)/x as x approaches 0 is 1, we can substitute that value in the expression:
lim (sin 4x)/3x = (4/3) * 1 = 4/3
Therefore, the answer to the given expression is 4/3.