Menu Close

lim-x-x-a-x-2-x-x-1-2-then-a-

Tinku Tara 0 Comments
Pin




Question Number 115103 by bobhans last updated on 23/Sep/20
lim_(x→∞) (√((x−a)(x+2))) −(√(x(x+1))) = 2 then a = ?
limx→∞(x−a)(x+2)−x(x+1)=2thena=?
Commented by Dwaipayan Shikari last updated on 23/Sep/20
lim_(x→∞) (((x−a)(x+2)−x^2 −x)/( x(√((1−(a/x))(1+(2/x))))+x(√(1+(1/x)))))=2 lim_(x→∞) ((x^2 −ax+2x−2a−x^2 −x)/(x+x))=2 lim_(x→∞) ((−a−1+2−((2a)/x))/2)=2 −a+1=4 a=−3 Or x(√((1−(a/x))(1+(2/x)))) −x(√(1+(1/x))) =2 x(1−(a/(2x))+(1/x)−(a/(2x^2 ))−1−(1/(2x)))=2 ((1−a)/2)−(a/(2x))=2 1−a=4 a=−3
limx→∞(x−a)(x+2)−x2−xx(1−ax)(1+2x)+x1+1x=2limx→∞x2−ax+2x−2a−x2−xx+x=2limx→∞−a−1+2−2ax2=2−a+1=4a=−3Orx(1−ax)(1+2x)−x1+1x=2x(1−a2x+1x−a2x2−1−12x)=21−a2−a2x=21−a=4a=−3
Answered by bemath last updated on 23/Sep/20
lim_(x→∞) (√(x^2 +(2−a)x−2a))−(√(x^2 +x)) = 2 ⇒ ((2−a−1)/(2.1)) = 2 ; 1−a = 4 ⇒a = −3
limx→∞x2+(2−a)x−2a−x2+x=2⇒2−a−12.1=2;1−a=4⇒a=−3
Answered by ruwedkabeh last updated on 23/Sep/20
lim_(x→∞) (√((x−a)(x+2))) −(√(x(x+1))) = 2 ⇔lim_(x→∞) (√(x^2 +(2−a)x−2)) −(√(x^2 +x)) = 2 ((2−a−1)/(2(√1)))=2⇒((1−a)/2)=2⇒1−a=4⇒a=−3
limx→∞(x−a)(x+2)−x(x+1)=2⇔limx→∞x2+(2−a)x−2−x2+x=22−a−121=2⇒1−a2=2⇒1−a=4⇒a=−3
Answered by Bird last updated on 24/Sep/20
let g(x) =(√((x−a)(x+2)))−(√(x(x+1))) ⇒g(x) =∣x∣(√(1−(a/x))).(√(1+(2/x))) −∣x∣(√(1+(1/x)))∼∣x∣{1−(a/(2x))} −∣x∣{1+(1/(2x))} =∣x∣−a ((∣x∣)/(2x))−∣x∣−((∣x∣)/(2x)) lim_(x→+∞) g(x)=2 ⇒ −(a/2)−(1/2) =2 ⇒−a−1 =4 ⇒ a+1 =−4 ⇒a=−5 lim_(x→−∞) g(x)=2 ⇒ (a/2)+(1/2)=2 ⇒a+1 =4 ⇒a=3
letg(x)=(x−a)(x+2)−x(x+1)⇒g(x)=∣x∣1−ax.1+2x−∣x∣1+1x∼∣x∣{1−a2x}−∣x∣{1+12x}=∣x∣−a∣x∣2x−∣x∣−∣x∣2xlimx→+∞g(x)=2⇒−a2−12=2⇒−a−1=4⇒a+1=−4⇒a=−5limx→−∞g(x)=2⇒a2+12=2⇒a+1=4⇒a=3
Commented by bemath last updated on 24/Sep/20
if a = 3 lim_(x→∞) (√(x^2 −x−6))−(√(x^2 +x)) = ((−1−1)/(2.1))=−1 wrong. your answer wrong. if lim_(x→∞) ∣x∣ = lim_(x→∞) x , but lim_(x→−∞) ∣x∣ = lim_(x→−∞) −x
ifa=3limx→∞x2−x−6−x2+x=−1−12.1=−1wrong.youranswerwrong.iflimx→∞∣x∣=limx→∞x,butlimx→−∞∣x∣=limx→−∞−x

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *