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## Homework Statement

see attachment- have to do this because i cant figure out how to do the notation in this part sorry....... I have no idea where to go with this and probably need quite a bit of help with it--- thanks.

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- Thread starter pat666
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see attachment- have to do this because i cant figure out how to do the notation in this part sorry....... I have no idea where to go with this and probably need quite a bit of help with it--- thanks.

- #2

HallsofIvy

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[tex]\lim\frac{\delta y}{\delta x}[/tex]

Do you know what that means?

[tex]\frac{\delta y}{\delta x}= \frac{y(1+ \delta x)- y(1)}{\delta x}[/tex]

[itex]y(1)= 1^2- 1= 0[/itex] and [itex]y(1+ \delta x)= (1+ \delta x)^2- (1+ \delta x)[/itex].

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- #4

Mark44

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It might be helpful to use function notation, letting f(x) = y = x

[tex]\lim_{\Delta x \to 0} \frac{f(1 + \Delta x) - f(1)}{\Delta x}[/tex]

The fraction gives the slope of a secant line between (1, f(1)) and (1 + [itex]\Delta x[/itex], f(1 + [itex]\Delta x[/itex])). The numerator gives the vertical change (rise) and the denominator gives the horizontal change (run). As [itex]\Delta x[/itex] approaches zero, the slope of the secant line approaches the slope of the tangent line.

Substitute for f(1) and f(1 + [itex]\Delta x[/itex]) in the limit formula above, simplify, and then take the limit.

If you still don't understand, your text should have an explanation of this and some examples.

- #5

Mark44

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BTW, you should post calculus problems (like this one) in the Calculus & Beyond section.

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