Question

If limx→∞(x2+x+1x+1−px−q)=−3, then p and q is:

• A. (A) p = 1, q = 3
• B. (B) p = 2, q = 3
• C. (C) p = 3, q = 1
• D. (D) p = 3, q = 2

Answer 1

Answer: (A)

(A) p = 1, q = 3

Answer 2

Explanation:
Given: limx→∞(x2+x+1x+1−px−q)=−3On simplifying, we get:⇒limx→∞(x2+x+1−px2−px−qx−qx+1)=−3⇒limx→∞(x2(1−p)+x(1−p−q)+1−qx+1)=−3 As we can see limit gives finite value. So, this is possible only when the coefficient of higher degree term will be zero.Therefore, (1−p)=0Or, p=1⇒limx→∞(x(1−p−q)+1−qx+1)=−3 ....(1)Dividing and multiplying by x in both numerator and denominator, we get:⇒limx→∞(x[(1−p−q)+(1−q)x]x[1+1x])=−3⇒limx→∞([(1−p−q)+(1−q)x][1+1x])=−3⇒([(1−p−q)+0][1+0])=−3⇒(1−p−q)=−3 ⇒(1−1−q)=−3(∵p=1)∴q=3Hence, the correct option is (A).