how do i find the limit?

Question

how do i find the limit?

lim (sin 5x) / (sin7x)
X->0

Answer 1

lim (x ---> 0) of (sin 5x) / (sin7x)
Use L'Hospital's rule
lim (x ---> 0) of (sin 5x) / (sin7x) =
lim (x ---> 0) of (5cos5x) / (7cos7x) =
5cos(0)/7cos(0) = 5/7

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L’Hospital’s Rule tells us that if we have an indeterminate form 0/0 (in this case) all we need to do is differentiate the numerator and differentiate the denominator and then take the limit.

Answer 2

We know that lim x --> sin(x) = x. So, for every reals a and b <>0, we have lim sin(ax)/sin(bx) = lim [(a sin(ax)/(ax)]/[ [(b sin(bx)/(bx)] = (a/b) [lim sin(ax)/(ax)]/[limsen(bx)/(bx)] = a/b * 1/1 = a/b.

So, your limit is 5/7