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Section 2.10 : The Definition of the Limit

Use the definition of the limit to prove the following limits.

1. \(\mathop {\lim }\limits_{x \to 3} x = 3\) Solution
2. \(\mathop {\lim }\limits_{x \to - 1} \left( {x + 7} \right) = 6\) Solution
3. \(\mathop {\lim }\limits_{x \to 2} {x^2} = 4\) Solution
4. \(\mathop {\lim }\limits_{x \to - 3} \left( {{x^2} + 4x + 1} \right) = - 2\) Solution
5. \(\displaystyle \mathop {\lim }\limits_{x \to 1} \frac{1}{{{{\left( {x - 1} \right)}^2}}} = \infty \) Solution
6. \(\displaystyle \mathop {\lim }\limits_{x \to {0^ - }} \frac{1}{x} = - \infty \) Solution
7. \(\displaystyle \mathop {\lim }\limits_{x \to \infty } \frac{1}{{{x^2}}} = 0\) Solution