What is the instantaneous rate of change of #f(x)=x-e^(5x-7) # at #x=0 #?
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The instantaneous rate of change of ( f(x) = x - e^{5x-7} ) at ( x = 0 ) is ( -4 ).
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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.
- How do you find the slope of the secant lines of #f(x) = (1/x) # through the points: (-4,(f(-4)) and (1,f(1))?
- How do you find the derivative of # F(x)=x^3−7x+5# using the limit definition?
- How do you use the limit definition to find the slope of the tangent line to the graph #F(x) = (( x^2) – 9) # at (2, -5)?
- What is the equation of the tangent line of #f(x) =tan^3x/x# at #x=pi/4#?
- What is the slope of the line normal to the tangent line of #f(x) = cscx-sin2x # at # x= (pi)/12 #?

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