How do you find the equation of the tangent line to the graph of the given function #f(x)= x/(x2)#; at (3,3)?
The first derivative of the function will give you the slope of this line
Use the quotient rule to differentiate the function
The equation of the line in point slope form will be
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To find the equation of the tangent line to the graph of the function f(x) = x/(x2) at the point (3,3), we can follow these steps:
 Find the derivative of the function f(x) using the quotient rule.
 Substitute the xcoordinate of the given point (3,3) into the derivative to find the slope of the tangent line.
 Use the pointslope form of a linear equation, y  y1 = m(x  x1), where (x1, y1) is the given point and m is the slope, to write the equation of the tangent line.
Let's go through these steps:

The derivative of f(x) = x/(x2) can be found using the quotient rule: f'(x) = [(x2)(1)  x(1)] / (x2)^2

Substitute x = 3 into the derivative to find the slope of the tangent line: f'(3) = [(32)(1)  3(1)] / (32)^2

Simplify the expression: f'(3) = [1  3] / 1^2 f'(3) = 2

Now we have the slope of the tangent line, which is 2, and the point (3,3). We can use the pointslope form to write the equation of the tangent line: y  3 = 2(x  3)

Simplify the equation: y  3 = 2x + 6

Rearrange the equation to the standard form: 2x + y = 9
Therefore, the equation of the tangent line to the graph of f(x) = x/(x2) at the point (3,3) is 2x + y = 9.
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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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