Question

Show that the function sin(x^3+7x+1) is continuous everywhere.

Answer 1

The theorem the book tells us to use is, If the function g is continuous everywhere and the function f is continuous everywhere, then the composition f of g is continuous everywhere.

Answer 2

so you need to show that sin(x) is continuous and x^3_7x+1 is continuous...do you need to show this with epsilon proof? do you have other theorems?
like
sin(x) is differentiable and thus continuous....

Answer 3

Um, the theorem that the book tells us to use to show that the function is continuous is: If the function g is continuous everywhere and the function f is continuous everywhere, then the composition f of g is continuous everywhere.

Answer 4

i get that, and we know that sin(x) and x^3-7x+1 are both continuous so the result follows

having said that

do we need to prove that sin(x) is continuous?
Is this for a epsilon delta type calculus class?

Answer 5

no, its just to show that the function is continuous.

Answer 6

@zzr0ck3r r u still available?

Answer 7

f(x) = sinx is continuous
g(x) = x^3-7x+1 is continuous
so by the theorem you stated
f(g(x)) = sin(g(x)) = sin(x^3-3x+1) is continuous