If y=a is a horizontal asymptote of the function y=f(x), then EITHER limlimits _(x→ ∞ )f(x)=a OR limlimits _(x→ -∞ )f(x)=a. Because either of these is sufficient for a horizontal asymptote at y=a, (A) might be true, but does not have to be true. (B) is one ...
then the function is a horizontal line, like {eq}\displaystyle f(x)=c, c- \text{ constant}. {/eq} If a limit at infinity of a function is zero, {eq}\displaystyle \lim_{x\to \infty}g(x)=0, {/eq} it means that t...
8. The horizontal asymptote ofy=(2x^2+x-1)/(x^2+x-2)is___.相关知识点: 试题来源: 解析 水平渐近线是 y = 2。 该函数的分子和分母最高次项都是 x^2,且系数分别为 2 和 1。当 x 趋向于无穷大时,函数的值将趋向于分子和分母最高次项系数的比值,即 2/1。因此,水平渐近线为 y = 2。反馈...
Question: What is {eq}c {/eq} if the line {eq}y = c {/eq} is a horizontal asymptote of {eq}f(x) = \dfrac{5(x + 1)(2x - 7)}{12(x - 1)(x - 4)} {/eq}? Horizontal Asymptotes: The behavior of a real-valued function of one variabl...
k is the horizontal asymptote Take a look at the function: {eq}f(x)=x+7 {/eq} The inverse of this function is: {eq}\frac{1}{x+7} {/eq} This is almost in the standard form for reciprocal functions: a = 1 x = x h = -7 k = ? Since there are no other ...
Therefore, the graph has a horizontal asymptote that is equal to y = 0. Intercepts The x-intercept does not exist since the graph never crosses x-axis. The y-intercept is (0,a) since y = ab0 = a(1) = a. For example, if the exponential function is y = 3x, the y-intercept ...
Thus, an asymptote can be defined as a line that is the limiting position of a tangent to a curve as its point of contact recedes indefinitely along an infinite branch of the curve. Types of Asymptotes There are three types of asymptotes. They are horizontal asymptotes, vertical asymptotes ...
To find the horizontal asymptote, you need to see what happens when x gets must larger (to oo) or much (to -oo). With the numerator and denominator expanded, f(x)=(2x^(2)+5x-3)/(x^(2)+6x+9). Divide both by x^(2) to see that y approaches 2 as x gets much
Prove or disprove: If f is an increasing function on (0, infty) whose graph is concave down throughout (0, infty), then the graph of f has a horizontal asymptote. Show that f(x) = ln x^n / x is a decreasing function for x greater than ...
The horizontal asymptote of f(x)=(ex+x)3x is a. y = 2 b. y = 3 c. y=e3 d. y = e Asymptotes: A function exhibits a horizontal asymptote at y=k if it tends to k as x approaches infinity. A vertical asymptote occurs at x=c if the cu...