What is the equation of the line that is normal to #f(x)=-sinx +tanx # at # x=-pi/3#?
First, find the point the normal line will intercept:
To find the slope of the normal line, we must first find the slope of the tangent line. Since the normal line and tangent line are perpendicular, their slopes will be opposite reciprocals.
The derivative of the function is
The slope of the tangent line is
Graphed are the original function and its normal line:
graph{(y+sinx-tanx)(y+sqrt3/2+2/7(x+pi/3))=0 [-4.858, 2.94, -2.89, 1.007]}
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The equation of the line that is normal to f(x)=-sinx +tanx at x=-pi/3 is y = -√3x - 2√3.
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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.
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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