Evaluating Limits

The process of evaluating limits is a critical aspect of calculus, aimed at deciphering how functions behave as their inputs draw near to a specific value. This critical concept aids in ascertaining the value a function gravitates towards as the input approaches a particular number from both left and right directions, almost infinitely.

Evaluating Limits Approaching a Value

Evaluate each limit. \[ \lim _{x \rightarrow-3^{+}} f(x), f(x)=\left\{\begin{array}{ll} -x^{2}-4 x-5, & x<-3 \\ \frac{x}{2}-5, & x \geq-3 \end{array}\right. \]
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Evaluating Limits Approaching Infinity

Find the limit of the following sequence or determine that the sequence diverges. \[ \left\{\frac{4 n}{\sqrt{49 n^{2}+6}}\right\} \]
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Using the Limit Definition to Find the Tangent Line at a Given Point

Find the equation of the tangent line to the curve \(y = x^3 - 3x^2 + 2\) at the point \((1,0)\)
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Popular Problems

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