Find the slant asymptote of the following function: To find the slant asymptote, I need to do the long division: I need to remember that the slant asymptote is the polynomial part of the answer (that is, the asymptote is the part across the top of the division, set equal to y), not...
The function has horizontal asymptotes if these limits are finite; if the limits are infinite or otherwise do not exist, no asymptote is present. Answer and Explanation: Taking the limit of the given function as {eq}x\to \infty{/eq}, we ...
The slant or oblique asymptote is an asymptote to the curve which is neither vertical nor horizontal. In general, such oblique asymptote exists when the degree of the polynomial in the numerator is higher than the polynomial in the denominator in the given function. In ...
find the horizontal asymptotes {eq}f(t)= \frac{3^t}{1+3^{-t}}{/eq} Horizontal asymptotes An asymptote is a line that a curve approaches. They can be horizontal, vertical or oblique. We can get the horizontal asymptote by studying the limit of the function {eq}\displaystyl...
Let's look at an example of finding horizontal asymptotes: Find the horizontal asymptote of the following function: y=x+2x2+1\small{ \boldsymbol{\color{green}{y = \dfrac{x + 2}{x^2 + 1} }}}y=x2+1x+2 First, notice that the denominator is a sum of squares, so it doesn...
This is because the points on the line will make the function undefined. In this problem, we are given a rational function. A rational function has a vertical, horizontal, or slant asymptote. Answer and Explanation: 1 We are given the raitional function {eq}f(x) = \dfrac{x^2 + 4}...
of the denominator is higher, the horizontal asymptote is y = 0; 3) if the degrees are equal, the horizontal asymptote is equal to the ratio of the leading coefficients; 4) if the degree of the numerator is one greater than the degree of the denominator, there is a slant asymptote. ...
Learn about slant asymptotes, what they look like, and the rules to calculate them. Understand how to find a slant asymptote with different examples provided. Related to this QuestionFind the following for the given function f(x). Find the following for the function f(x) = |...
Consider the function f(x)=(6x3+9x2+3x+1)(4x2+7x+3) (a) Find the equation of the non-vertical asymptote (b) Does f(x) intersect its non-vertical asymptote? If so, what is the smallest value of x at which f(x) intersects its non-vertical asymptote?
Properties of function: This problem involves finding the domain, intercepts, and asymptotes of a given function. The domain is nothing but the acceptable values of the input variable such that the output value of the function is finite and real. The intercepts are all the points ...