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

Simplifying is left up to the reader's imagination.

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The equation of the tangent line of f(x) = e^xlnx-x at x=2 is y = 2e^2ln2 - 2.

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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.

- Is the x-axis tangent to #y = x^3#?
- Sketch the parabolas #y=x^2# and #y=x^2-2x+2#, do you think there is a line that is tangent to both curves?
- The graph of the function #(x^2 + y^2 + 12x + 9)^2 = 4(2x + 3)^3# is a Tricuspoid as shown below. (a) Find the point on the curve, above x-axis, with x = 0? (b) Find slope of tangent line to the point in part (a)?
- How do you find f'(x) using the definition of a derivative for #f(x)=(x+1)/(x-1) #?
- How do you find the slope of the tangent line to the curve at (1,0) for #y=x-x^2#?

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