Previous Year Questions on Asymptotes

Asymptotes - Previous Year Questions

Previous Year Questions on Asymptotes

Previous year questions on Asymptotes provide invaluable insights into this critical concept in Differential Calculus Notes. Asymptotes, rooted in the history of mathematical analysis, have played an essential role in understanding the behavior of curves at extreme values. This topic is significant for both theoretical and practical applications in various fields.

Vidyasagar University

2023-24 (NEP)

Prove that \(y=ax+b \) is an asymtote to the curve \(y=ax+b+\frac{\sin{x}}{x} \). [2]
Determine the asymptotes of the curve \(x=\frac{1}{t^{4}-1} \) and \(y=\frac{t^{3}}{t^{4}-1} \). [3]

2023-24 (CBCS)

Find the asymptotes of \(x^{3}-x^{2}y-xy^{2}+y^{3}+2x^{2}-4y^{2}+2xy+x+y+z=0 \). [5]

2022-23 (CBCS)

2021-22 (CBCS)

Find the equation of the asymptotes of the curve \(r^{n}f_{n}(\theta)+r^{n-1}f_{n-1}(\theta)+…+f_{0}(\theta)=0 \). [5]
Find the asymptotes of the parametric curve \(x=\frac{t^{2}+1}{t^{2}-1} \) and \(y=\frac{t^{2}}{t-1} \). [4]
Find all the asymptotes, if any of the curve \(y=a\log{\sec{\left(\frac{x}{a}\right)}} \). [2]

2020-21 (CBCS)

Show that the four asymptotes of the curve \(\left(x^{2}-y^{2} \right)\left(y^{2}-4x^{2} \right)+6x^{3}-5x^{2}y-3xy^{3}+2y^{3}-x^{2}+3xy-1=0 \) cut the curve in eight points which lie on the circle \( x^{2}+y^{2}=1\). [6]
What do you mean mean by rectillinear asymptotes to a curve ? [4]
Find the asymptotes of the curve \(\left(x+y \right)\left(x-2y \right)\left(x-y \right)^{2}+3xy\left(x-y \right)+x^{2}+y^{2}=0 \). [6]

2019-20 (CBCS)

Find the oblique asymptotes of the curve \(y=\frac{3x}{2}\log{\left[e-\frac{1}{3x}\right]} \). [2]
The parabolic path is given by \(y=x\tan{\theta}-\frac{x^{2}}{4h\cos^{2}{\theta}}\), What will be the asymptote of parabolic paths? [2]

2018-19 (CBCS)

Find all the asymptotes, if any of the curve \(y=a\log{\sec{\left(\frac{x}{a}\right)}} \). [2]
Find the asymptotes of the curve \(x^{3}-2x^{2}y+xy^{2}+x^{2}-xy+2=0 \). [3]

2017-18 (CBCS)

What do you mean by asymptote? Does asymptote exists for every curve? [2]

FAQs

What is an asymptote?
An asymptote is a line that a curve approaches infinitely closely but never touches. Learn more in Mathematics Notes.
What are the types of asymptotes?
The three types are vertical, horizontal, and oblique asymptotes. Check examples in Differential Calculus Questions.
How is an asymptote identified?
Asymptotes are determined by analyzing the limits of the function at infinity.
Where are asymptotes used?
Asymptotes are used in calculus, physics, and economic modeling.
How do asymptotes relate to limits?
They describe the behavior of a function as it approaches infinity or a particular value.
Can a curve have multiple asymptotes?
Yes, a curve can have one or more asymptotes, depending on its equation.
What is an oblique asymptote?
It is a slanted line approached by the curve when the degree of the numerator exceeds the degree of the denominator.
What role do asymptotes play in graphing?
Asymptotes help define the overall shape and behavior of the graph of a function.
How are asymptotes different from tangents?
Tangents touch the curve, while asymptotes are lines the curve approaches but does not touch.
Are asymptotes only for rational functions?
No, asymptotes can appear in exponential, logarithmic, and other types of functions as well.