lim [exp(( sinx) / x )]
x-> infinity
answer is 1
x-> infinity
answer is 1
-
Using a calculator should never be your first choice. Note that for all x > 0
-1/x ≤ sin(x)/x ≤ 1/x
because |sin(x)| ≤ 1. As both -1/x and 1/x tend to zero as x ->∞,
lim sin(x)/x = 0.
x->∞
As the function f(t) = e^t, is continuous,
lim exp(sin(x)/x) = exp(0) = 1.
x->∞
-1/x ≤ sin(x)/x ≤ 1/x
because |sin(x)| ≤ 1. As both -1/x and 1/x tend to zero as x ->∞,
lim sin(x)/x = 0.
x->∞
As the function f(t) = e^t, is continuous,
lim exp(sin(x)/x) = exp(0) = 1.
x->∞