Prove that the product of two continuous functions is continuous. $(\varepsilon, \delta)$
125682
Proof verification: the product of two continuous functions is continuous
55605
If $f_n(x_n) \to f(x)$ whenever $x_n \to x$, show that $f$ is continuous
15914
Prove that any polynomial function is continuous
151573
Show f is continuous on (0, ∞) iff f is continuous at 1 for a defined function.
62270
Given two increasing continuous functions $f,g$ prove that $(b-a) \int^b_a f(x)g(x) dx > \int^b_a f(x) dx \int^b_a g(x) dx$
143174
property of continuous function
64619
Continuity of a function of product spaces
130023
Prove that the sum of two continuous functions is continuous
12408
Prove that a function whose derivative is bounded is uniformly continuous.
85623
Proof of continuity implied by differentiability
62887
Proof that a linear transformation is continuous
118332
proof $f(\overline{A})\subseteq \overline{f(A)} \Leftrightarrow f$ continuous
40297
Proof of uniform limit of Continuous Functions
115077
Prove continuity for cubic root using epsilon-delta
105084
Let f be a function twice differentiable and with derivatives continuous on an interval $[a,b]$ containing $0$. Prove the following statement:
14896
Prove: the set of zeros of a continuous function is closed.
109896
Proving that the function $f(x,y)=\frac{x^2y}{x^2 + y^2}$ with $f(0,0)=0$ is continuous at $(0,0)$.