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

Write in point-slope form:

In slope-intercept form:

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The equation of the tangent line of f(x) = xe^(x)-x^2+x at x=3 is y = 10e^3 - 9x + 3.

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To find the equation of the tangent line to the function (f(x) = xe^x - x^2 + x) at (x = 3), follow these steps:

- Find the slope of the tangent line by evaluating the derivative of the function at (x = 3).
- Use the point-slope form of a line, (y - y_1 = m(x - x_1)), where (m) is the slope found in step 1, and ((x_1, y_1)) is the point of tangency, which is ((3, f(3))).
- Substitute the values into the equation to find the equation of the tangent line.

So, first, find (f'(x)), then evaluate it at (x = 3) to get the slope. Afterward, substitute (x = 3) into the original function to find the corresponding (y)-coordinate. Finally, use the point-slope form to write the equation of the tangent line.

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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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