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 \to - 3^{+}} f (x), f (x) = {\begin{cases} - x^{2} - 4 x - 5, & x < - 3 \\ \frac{x}{2} - 5, & x \geq - 3 \end{cases}

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Evaluating Limits Approaching Infinity

Find the limit of the following sequence or determine that the sequence diverges.

{\frac{4 n}{\sqrt{49 n^{2} + 6}}}

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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} - 3 x^{2} + 2

at the point

(1, 0)

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Evaluating Limits

Evaluating Limits Approaching a Value

Evaluating Limits Approaching Infinity

Using the Limit Definition to Find the Tangent Line at a Given Point

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