Solved Problems

Tag: rational function

Problem 2-9: Differentiating Polynomial and Rational Functions

Differentiate
a) $f\left(x\right)= 1+ 2x$
b) $f\left(x\right)= 1 - 2x + 2x^2$
c) $f\left(x\right)= 1- x^2 +\frac{1}{x}$
d) $f\left(x\right)= 1 - x +\frac{1}{1-x}$

Solution
The following rules can be used:
I) $\displaystyle\frac{d}{dx}ax^n=anx^{n-1}$
II) $\displaystyle\frac{d}{dx}\left(u+v\right)=\frac{du}{dx}+\frac{dv}{dx}$
III) $\displaystyle\frac{d}{dx}\frac{u}{v}=\frac{1}{v^2}\left(v\frac{du}{dx}-u\frac{dv}{dx}\right)$
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April 11, 2010
Problem 2-4: Computing Limits of a Rational Function

Compute
a) $\displaystyle\lim_{x\to 3}\frac{x^2+2x-3}{x+3}$
b) $\displaystyle\lim_{x\to -3}\frac{x^2+2x-3}{x+3}$

Solution

a) $\displaystyle\lim_{x\to 3}\frac{x^2+2x-3}{x+3}=\frac{3^2+2\times 3-3}{3+3}=2$
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April 9, 2010