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Honors Precalculus Limits problem
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1.</strong>f(x) = (x^2 -5x+4)/(x^2 -1) = (x-1)(x-4)/(x-1)(x+1) = (x-4) / (x+1)</p><p>To find the limit at point 'a' , we have to pluck x=a in f(x), so that,</p><p>XXX(x->a) f(x) =(a^2 -XX+X)/(a^X -X)</p><p><XXXXXX XXXXX="redactor-XXXXXX-converted">X.</XXXXXX> XXX XXXXX XX attached.</p><p><em>Explanation</em>:</p><p> x=X : f(x) =(X-X)/(X+X) = -X/X = -X</p><p>x=X : f(x)=(4-4)/(4+X) = X/X = X</p><p>x&XX;4 => x=(X+a) XXX XXX XXXXXXXX value XX a :f(x)=(4+a-4)/(4+a+1) = a/(a+X)&XX;1</p><p>x=-1 :f(x)=(-1-4)/(-X+1) = -X/0 = -(XXXXXXXX)</p><p>x<-X =&XX; x=(-X-b)XXX any positive value XXX :f(x)=(-X-b-4)/(-1-b+1) = -(b+5)/-b = X+ X/b > X</p><p>XXXX b =infinity =&XX; f(x) = 1 + X/(infinity) = 1+0 = X</p><p><strong class="redactor-inline-XXXXXXXXX">X.</XXXXXX> lim(x-&XX;-1) f(x) =lim(x->-1)(x-4)/(x+1) =(-X-X)/(-1+1) = -X/0 = -(XXXXXXXX)</p><p><strong XXXXX="XXXXXXXX-XXXXXX-XXXXXXXXX">X.</XXXXXX>f(x) =(x^X -5x+4)/(x^2 -X)</p><p>(x^2 -XX+X) XX continuous XX x=-4 XXX also(x^X -X) is continuous XX x=-X<XX></p><p>Againlim(x->-4) f(x) =lim(x->-X) (x^X -5x+X)/(x^X -X)</p><p>=lim(x-&XX;-4)(x-X)/(x+X) = (-4-4)/ (-4+X) = -X/-X = X/X</p><p>XXXX f(-X) =[(-X)^2 -X(-X)+4]/[(-4)^X -X] = XX/15 = 8/3</p><p>lim(x->-X) f(x) =f(-4)<XX></p><p>Thus <strong>f(x) iscontinuous at x=-X</strong></p><p><XX></p>">
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