# How do you find the equation of the tangent and normal line to the curve #y=x^(1/2)# at x=1?

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We find the tangent line to a curve by finding the derivative first.

Power rule:

A normal line is perpendicular to the tangent line.

We can find the slope of the normal line by finding the negative reciprocal of the slope of the tangent line.

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To find the equation of the tangent line to the curve ( y = \sqrt{x} ) at ( x = 1 ), you first need to find the slope of the tangent line by taking the derivative of the curve at ( x = 1 ). Then, you can use the point-slope form of the equation of a line to find the equation of the tangent line. Similarly, to find the equation of the normal line, you use the negative reciprocal of the slope of the tangent line. Here are the steps:

- Find the derivative of the curve ( y = \sqrt{x} ).
- Evaluate the derivative at ( x = 1 ) to find the slope of the tangent line.
- Use the point ( (1, \sqrt{1}) = (1, 1) ) and the slope found in step 2 to write the equation of the tangent line using the point-slope form.
- To find the equation of the normal line, take the negative reciprocal of the slope found in step 2 and use the same point ( (1, 1) ) to write the equation using the point-slope form.

After these steps, you will have the equations of both the tangent and normal lines to the curve ( y = \sqrt{x} ) at ( x = 1 ).

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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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