Limits

Practice Questions

Calculus 3 › Limits

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$\begin{align*}&\text{Calculate the limits of the function}\&\lim_{(x,y)\rightarrow(0+,0-)}\frac{(18xy^{3})}{(19x^{4} + 18y^{4})}\&\text{along the y-axis and the line, }y=x\end{align*}$

$\begin{align*}&\text{Evaluate the following limit:}\&lim_{x\rightarrow-8-}-\frac{(2970x - 693x^{2} - 54x^{3} + 9x^{4} + 3600)}{(312x + 6x^{2} - 6x^{3} - 960)}\end{align*}$

$\begin{align*}&\text{Evaluate the following limit:}\&lim_{x\rightarrow-4+}-\frac{(1260x + 240x^{2} + 15x^{3} + 2160)}{(384x + 432x^{2} - 12x^{4} - 2304)}\end{align*}$

$\begin{align*}&\text{Evaluate the following limit:}\&lim_{x\rightarrow8-}-\frac{(13200x + 7403x^{2} - 803x^{3} - 99x^{4} + 11x^{5} - 123200)}{(1456x^{2} - 13088x + 128x^{3} - 16x^{4} + 11520)}\end{align*}$

$\begin{align*}&\text{Evaluate the following limit:}\&lim_{x\rightarrow10+}\frac{(13x^{2} - 260x + 1300)}{(9x^{2} - 108x + 180)}\end{align*}$

$\begin{align*}&\text{Calculate the limits of the function}\&lim_{(x,y)\rightarrow(0-,0+)}-\frac{(9x^{4}y^{2} + 9xy^{5} - 18x^{6})}{(3x^{6} + 2y^{6})}\&\text{along the x-axis and the line, }y=x\end{align*}$

$\begin{align*}&\text{Calculate the limits of the function}\&lim_{(x,y)\rightarrow(0-,0-)}-\frac{(2x^{3}y^{3} + x^{5}y - 3x^{6})}{(3x^{6} + y^{6})}\&\text{along the x-axis and the line, }y=x\end{align*}$

$\begin{align*}&\text{Calculate the limits of the function}\&lim_{(x,y)\rightarrow(0-,0-)}-\frac{(13x^{2}y^{4} - 19x^{5}y + 6x^{6})}{(2x^{6} + 3y^{6})}\&\text{along the x-axis and the line, }y=x\end{align*}$

$\begin{align*}&\text{Evaluate the following limit:}\&lim_{x\rightarrow13}-\frac{(x - 13)}{(12x - x^{2} + 13)}\end{align*}$

$\begin{align*}&\text{Calculate the limits of the function}\&\lim_{(x,y)\rightarrow(0-,0-)}\frac{(21xy^{2} - 18y^{3})}{(14xy^{2} - 12x^{3} + 17y^{3})}\&\text{along the y-axis and the line, }y=x\end{align*}$

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