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Questions › DSE › DSE 2019 › Q6
0 marksMathematics › Limits, continuity and differentiability › Asymptotes and behaviour of functionsModerateabout 2 min

DSE 2019 Question 6: Limits, continuity and differentiability

lim⁡x→∞(x2−x+1x+1−c1x−c2)=−5\lim_{x\to\infty}\left(\dfrac{x^{2}-x+1}{x+1}-c_{1}x-c_{2}\right)=-5limx→∞​(x+1x2−x+1​−c1​x−c2​)=−5. So, it must be that (c1,c2)(c_{1},c_{2})(c1​,c2​) equals

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lim_(x→∞)((x²-x+1)/(x+1)-c₁x-c₂)=-5. So, it must be that (c₁,c₂) equals (A) (1,3) (B) (2,-3) (C) (1,2) (D) (2,3)

Also written as: lim_(x-> inf)((x^2-x+1)/(x+1)-c_1x-c_2)=-5. So, it must be that (c_1,c_2) equals

Limits, continuity and differentiability has come up 122 times in 7 exams since 2006.

What this question tests

This question is on Asymptotes and behaviour of functions, part of Limits, continuity and differentiability in Mathematics.

How functions behave at infinity and near points where they are undefined.

TestStop has 3 past-paper questions on this subtopic.

Practise Limits, continuity and differentiabilityMore on Asymptotes and behaviour of functions

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Question from the DSE 2019 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.