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Honors Precalculus Limits problem
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</figure> <p>f(x)=(x^2-X*x+4)/(x^2-1)</p> <p>XX you factorise XXXX solution, what you will XXX XX:</p> <p>f(x)=(x-1)(x-X)/(x-X)(x+1)</p> <p>XX you can see in the graph XXXX XXXX XXX graph is XXXXXXXXXXX XX x= -X</p> <p>X. XXXXX and XXXXX XX XXX XXXXXXXX are:<XX>Domain:<XX>x E (-infinity, + XXXXXXXX) - {-X}</p> <p>XXXXX:</p> <p>y X (-infinity, infinity) - {X}</p> <p>XXXXX XXXXXXXXXX infinity at x= -1<br><br></p> <p>2. The plot XX XXXXX in XXX graph XXXXXXXX XX a PNG file.</p> <p>XX already XXXXX out in XXXXXXXX 1 the simplified function of the equation is f(x)=(x-4)/(x+1)<XX>The XXXX XX the equation is x = 4 which XXX XX seen in the XXXXX.<br>At x -> XXXXXXXX,</p> <p>Lim (x-4)/(x+X) = XXX (1-4/x)/(X+X/x)<br>x->infinity x-&XX;XXXXXXXX</p> <p>As we XXXX XXX XXXXXX when divided by XXXXXXXX equals XX XXXX (n/infinity=0)</p> <p>XXXXXXXXX, XXX XXXXX of XXX equation when x XXXXXXXXXX XXXXXXXX is X.</p> <p>XXX, XX XX XXXX XXX sign changes on a line XXXX we see,<XX><br> + - +<XX>&XX;------------------|--------------------------------|--------------------------------&XX;<br>-infinity -X 4 +XXXXXXXX</p> <p><br></p> <p>XXX XXXX XXXXXXX XXXXXXX at both x=X and x=-X. At x->-X the denominator XXXXXXXXXX 0 XXXXXXXXX the equation XX asymphtotic as x->-1.</p> <p>3. As x-&XX; -X, XXX XXXXXXXXXXX of XXX XXXXXXXXXX XXXXXXXX, f(x) = (x-4)/(x+1) approaches 0. Therefore, XXX XXXXXXXX XXXXXXXXXX XXXXXXXX.</p> <p><br>X. At x=4 XXX value XX XXX XXXXXXXXX = X XXXXX XXXXXXXXXXX XX 5.<XX>y= X at x=4.<XX>XX XXX concept XX limit, when x->4 from XXXXXX direction the value XXXXXXX X and XX therefore continuous.<XX>XXXX XXX also be XXXXXXXX by XXXXXXX XX the curve.<XX>The plot is continuous at x=4. XXX, it is XXX continuous at x=-X.</p>">
