How do you find the equation of the line tangent to the graph of #y = sqrtx# at (16,4)?
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To find the equation of the line tangent to the graph of y = sqrt(x) at the point (16,4), we can use the derivative of the function.
First, we find the derivative of y = sqrt(x) with respect to x, which is 1/(2*sqrt(x)).
Next, we substitute x = 16 into the derivative to find the slope of the tangent line at that point.
The slope of the tangent line is 1/(2*sqrt(16)) = 1/8.
Using the pointslope form of a linear equation, we have y  4 = (1/8)(x  16).
Simplifying the equation, we get y = (1/8)x + 2.
Therefore, the equation of the line tangent to the graph of y = sqrt(x) at (16,4) is y = (1/8)x + 2.
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To find the equation of the line tangent to the graph of (y = \sqrt{x}) at the point (16,4), you need to find the slope of the tangent line at that point, then use pointslope form to write the equation of the tangent line.

Find the derivative of the function (y = \sqrt{x}). [ \frac{dy}{dx} = \frac{1}{2\sqrt{x}} ]

Evaluate the derivative at x = 16 to find the slope of the tangent line at that point. [ \frac{dy}{dx} \bigg_{x=16} = \frac{1}{2\sqrt{16}} = \frac{1}{8} ]

Use the pointslope form of a line with point (16,4) and slope (\frac{1}{8}). [ y  y_1 = m(x  x_1) ] [ y  4 = \frac{1}{8}(x  16) ]

Simplify to get the equation in slopeintercept form, if necessary. [ y  4 = \frac{1}{8}x  2 ] [ y = \frac{1}{8}x + 2 ]
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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