GAIN AN ADVANTAGE
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- PDF: How to Make an A+ in Your First Calculus Course
Lesson Specific Problems
- 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 $a$ and $f(a)\neq 0$ then $1/f(x)$ is continuous at $a$.
- Prove that if \[\lim_{h\to 0}\,f(a+h)=f(a)\] then $f(x)$ is continuous at $a$.
- Prove that if $f(x)$ is continuous at $a$ then \[\lim_{h\to 0}\,f(a+h)=f(a).\]
- Prove that $f(x)$ is continuous at $a$ if and only if \[\lim_{h\to 0}\,f(a+h)=f(a).\]
