query: proving a function is continuous, $f(x)=x^5 + 2x^3 + 3x^2 + 6$
positive_passages.docid: 15914
positive_passages.text: Prove that any polynomial function is continuous
negative_passages.docid: 8836
negative_passages.text: If $f$ is continuous on $[a , b]$ and $\int_a^b f(x) p(x)dx = 0$ then $f = 0$
negative_passages.docid: 113871
negative_passages.text: Prove $f(x) = \sqrt x$ is uniformly continuous on $[0,\infty)$
negative_passages.docid: 109942
negative_passages.text: Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
negative_passages.docid: 23294
negative_passages.text: Show that the function $f = \frac{xy}{x^2 + y^2}$ is continuous along every horizontal and every vertical line
negative_passages.docid: 153730
negative_passages.text: Show that $f(x)=x^2$ is continuous at $a=2$ using the $\delta-\epsilon$ definition of continuity.
negative_passages.docid: 26388
negative_passages.text: proof that function is constant
negative_passages.docid: 127449
negative_passages.text: Uniform continuous of $f(x,y) = \sin(x^2+y)$
negative_passages.docid: 110146
negative_passages.text: I need to prove the continuity of $f(x)=\log x$ using a $\epsilon-\delta$ proof
negative_passages.docid: 56127
negative_passages.text: Prove a function is constant under certain conditions
negative_passages.docid: 46629
negative_passages.text: Prove if $f(x) = g(x)$ for each rational number x and $f$ and $g$ are continuous, then $f = g$
negative_passages.docid: 118207
negative_passages.text: Prove that the product of two continuous functions is continuous
negative_passages.docid: 105652
negative_passages.text: Suppose $f: \mathbb{R} \to \mathbb{R}$ is function such that $f^3$ is continuous on $\mathbb{R}$. Prove that $f$ is continuous on $\mathbb{R}$
negative_passages.docid: 145368
negative_passages.text: How to show $f:Y\to X^{+}$ is continuous?
negative_passages.docid: 75479
negative_passages.text: Proving that this function is continuous on $G\times G$
negative_passages.docid: 57180
negative_passages.text: Techniques to prove a function is uniformly continuous
negative_passages.docid: 124499
negative_passages.text: Where is the error in my proof that all derivatives are continuous?