# What is the equation of the tangent line of # f(x)=(x-1)^2 # at # x=3 #?

The gradient of the tangent to a curve at any particular point is give by the derivative of the curve at that point.

so If

#dy/dx = 2x-2#

When

and

So the tangent we seek passes through

# \ \ \ \ \ y-4=4(x-3) #

# :. y-4=4x-12#

# :. \ \ \ \ \ \ \ y=4x-8 #

We can confirm this solution is correct graphically:

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The equation of the tangent line of f(x)=(x-1)^2 at x=3 is y = 8x - 23.

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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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