GAIN AN ADVANTAGE
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- PDF: How to Make an A+ in Your First Calculus Course
Lesson Specific Problems
- Prove that if $f(x)$ is continuous on $[a,b]$ and $f(b)\lt 0\lt f(a)$, then there exists a number $K$ between $a$ and $b$ such that $f(K)=0$.
- Prove that if $f(x)$ is continuous at $a$ then there is an open interval around $a$ for which $f(x)$ is bounded.
- Prove that if $f(x)$ is continuous on $[a,b]$ and $f(a)\lt 0\lt f(b)$, then there exists a number $K$ between $a$ and $b$ such that $f(K)=0$.
- Prove that if $g(x)$ is continuous at $a$ and $f(x)$ is continuous at $f(g(a))$ then the function composition $(f\circ g)(x)$ is continuous at $a$.
- Prove that if $f(x)$ is continuous at $a$ then there is a closed interval around $a$ for which $f(x)$ is bounded.
