Chapter 2 :Limits and Continuity

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​If the degree of the numerator of a rational function is one greater than the degree of the denominator, the graph has an oblique(slanted)asymptote. We find an equation for the asymptote by dividing numerator by denominator to express f as a linear function plus a remainder that goes to zero as x\rightarrow\pm\infty. Here is an example.


The function f(x) = x is called the identity function.

All composites of continuous functions are continuous.


Answer:


Answer:


Answer:


At what points are the following functions continuous?

1. \frac{xtanx}{x^2+1}

2. \sqrt{2x+3} 3. \sqrt[4]{3x-1}

Answer:

  1. x\ne k\pi-\frac{\pi}{2} (k is any integer)

  2. x\geq-\frac{3}{2}

  3. x\geq\frac{1}{3}

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