Use the definition of continuous function to show that $f(x) = x^2 + 3$ is continuous at $x=3$.
72044
prove $x \mapsto x^2$ is continuous
54403
Given $f : \Bbb{R} \to \Bbb{R}$ is a continuous function. To prove that $\int_{0}^{1}f(x)x^2 dx = \frac{f(c)}{3}$ for some $c \in [0,1]$
109896
Proving that the function $f(x,y)=\frac{x^2y}{x^2 + y^2}$ with $f(0,0)=0$ is continuous at $(0,0)$.
104044
Prove continuous functions $f$ and $g$ are equal
44402
If $\{x:f(x) > a\}$ and $\{x:f(x) < a\}$ are open$\forall~a\in\mathbb{R}$ then f is continuous.
125682
Proof verification: the product of two continuous functions is continuous
130299
Prove that if a function $f: X\to Y$ continuous then its graph is closed
129856
Show that $f(x)=\frac{x}{1+|x|}$ is uniformly continuous.
139744
For a continuous function $f$ show $\exists c\in (0,1)$ s.t $f(c)=3c^2$
150554
proof that $f'$ is continuous at $a$
11158
Proof that a continuous function with $f(x) = f(x^2)$ is constant.
144614
If $f$ is continuous on $[a,b]$ and $F(x) = \sup f([a,x])$. Prove that $F$ is continuous on $[a,b]$ .
143174
property of continuous function
62947
If $f(x)$ is equal to $x$ or $1-x$ when $x$ is rational/irrational, then $f$ is continuous only at $x=1/2$
151427
f, g continuous for all rationals follow by continuous on all reals?
120947
continuous real-valued function
98772
Continuity of a function in $\mathbb{R}$