GAIN AN ADVANTAGE
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Lesson Specific Problems
- Prove that \[ \lim_{h\to 0}\,\sqrt{x+h}+\sqrt{x}=2\sqrt{x}. \]
- Prove that if \[\lim_{h\to 0}\,g(h)=0\] and $g(h)\neq 0$ for some interval $(-\bar{\delta},0)\cup (0,\bar{\delta})$ where $\bar{\delta}\gt 0$ then \[ \lim_{h\to 0}\,g(h)=\lim_{g(h)\to 0}\,g(h). \]
- Prove that if \[\lim_{h\to 0}\,f(a+h)=L, \] then \[\lim_{x\to a}\,f(x)=L.\]
- Prove that if \[\lim_{x\to a}\,f(x)=L,\] then \[\lim_{h\to 0}\,f(a+h)=L.\]
- Prove that \[\lim_{x\to a}\,f(x)=L\] if and only if \[\quad\lim_{h\to 0}\,f(a+h)=L.\]
