Differentiation, derivatives and Taylor approximations: Tangent line
Difference quotient in a point
- Calculate the difference quotient of the function \(f(x)=\frac{3}{x+3}\) over the interval \([-1,-1+h]\) for an indeterminate \(h>0\).
- What does the expression found in part (a) become when \(h\) gets negligibly small?
- Calculate the difference quotient of the function \(f(x)=\frac{3}{x+3}\) over the interval \([-1-h,-1]\) for an indeterminate \(h>0\).
- What does the expression found in part (c) become when \(h\) gets negligibly small?
| \(\frac{{\vartriangle}f}{{\vartriangle}x}\) over \([-1,-1+h]={}\) |
| \(\frac{{\vartriangle}f}{{\vartriangle}x}\) over \([-1,-1+h]\approx{} \) | when \(h\approx 0\). |
| \(\frac{{\vartriangle}f}{{\vartriangle}x}\) over \([-1-h,-1]={}\) |
| \(\frac{{\vartriangle}f}{{\vartriangle}x}\) over \([-1-h,-1]\approx{} \) | when \(h\approx 0\). |
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