How do you graph #y=5ln(3x)#?
y is defined for
graph{5ln(3x) [-23.1, 23.15, 46.2, 46.2]}
graph{5ln(3x) [-0.941, 0.983, 1.915, 1.927]}
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To graph ( y = 5 \ln(3x) ), follow these steps:
- Identify key points:
- Find the vertical asymptote: ( 3x = 0 ) implies ( x = 0 ). So, there's a vertical asymptote at ( x = 0 ).
- Determine behavior as ( x \rightarrow 0^+ ) and ( x \rightarrow +\infty ).
- Plot points:
- Choose values for ( x ) to the left and right of ( x = 0 ) to see the behavior.
- Calculate corresponding ( y ) values using the equation.
- Draw the graph:
- Connect the points smoothly, considering the behavior around the asymptote.
Remember, the graph will be a logarithmic curve that approaches the vertical asymptote at ( x = 0 ), and it will never intersect or go below the x-axis.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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