# How does linear growth differ from exponential growth?

Linear growth is always at the same rate, whereas exponential growth increases in speed over time.

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Linear growth is characterized by a constant rate of change, where the quantity increases or decreases by the same amount over equal intervals of time. In contrast, exponential growth is characterized by a constant relative growth rate, where the quantity increases or decreases by a fixed percentage over equal intervals of time. This means that exponential growth leads to a rapid increase in quantity over time, while linear growth leads to a steady and predictable change.

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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.

- How do you find the volume of the solid obtained by rotating the region bounded by the curves #y=x^3#, #y=1#and #x=2 # about the y axis?
- What is the arc length of #f(x) = x^2-ln(x^2) # on #x in [1,3] #?
- How do you find the volume of the solid obtained by rotating the region bounded by the curves #f(x) = 3x^2# and #f(x) = 5x+2 # about the x axis?
- How do you find the volume bounded by #y=(x^3)/3#, x=1, and the x-axis revolved about the x=axis?
- What is the arc length of #f(x)=(x^3 + x)^5 # in the interval #[2,3]#?

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