# What are some examples of non differentiable functions?

There are three ways a function can be non-differentiable. We'll look at all 3 cases.

Case 1 A function in non-differentiable where it is discontinuous.

graph{y=cotx [-10, 10, -5, 5]}

graph{(x^3-6x^2+9x)/(x^3-2x^2-3x) [-10, 10, -5, 5]}

Example 1d) description : Piecewise-defined functions my have discontiuities.

graph{abs(x-2) [-3.86, 10.184, -3.45, 3.57]}

graph{x+root(3)(x^2-2x+1) [-3.86, 10.184, -3.45, 3.57]}

Case 3

graph{2+(x-1)^(1/3) [-2.44, 4.487, -0.353, 3.11]}

graph{sqrt(4-x^2) [-3.58, 4.213, -1.303, 2.592]}

graph{x^(2/3) [-8.18, 7.616, -2.776, 5.126]}

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Some examples of non-differentiable functions include:

- Absolute value function (|x|)
- Step function (Heaviside step function)
- Modulus function (mod x)
- Sigmoid function (logistic function)
- The Weierstrass function
- The Dirichlet function

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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.

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