Algebra ExamplesPopular Problems Show Algebra Graph y = log of x Step 1 Find the asymptotes. Tap for more steps... Set the argument of the logarithm equal to zero. The vertical asymptote occurs at . Vertical Asymptote: Vertical Asymptote: Step 2 Find the point at . Tap for more steps... Replace the variable with in the expression. Simplify the result. Tap for more steps... Logarithm base of is . The final answer is . Convert to decimal. Step 3 Find the point at . Tap for more steps... Replace the variable with in the expression. Simplify the result. Tap for more steps... Logarithm base of is . The final answer is . Convert to decimal. Step 4 Find the point at . Tap for more steps... Replace the variable with in the expression. The final answer is . Convert to decimal. Step 5 The log function can be graphed using the vertical asymptote at and the points . Vertical Asymptote: Step 6 Algebra ExamplesPopular Problems Algebra Find the Asymptotes y = log of x Step 1 Set the argument of the logarithm equal to zero.
Step 2 The vertical asymptote occurs at . Vertical Asymptote: Step 3 #f(x)=log(g(x))# The Existence Condition is #g(x)>0# because #log# is definited #AAx in (0,+oo)# #g(x)=x+2# #x+2>0# #x> -2# Then: #F.E.# (Field of Existence): #(-2,+oo)# #x=x_0=-2# Could be a vertical asymptote if #lim_(x rarr-2^+) f(x)=+-oo# #lim_(x rarr-2^+) f(x)=lim_(x rarr-2^+) log(x+2)=# #lim_(x rarr-2^+) log(0^+)=-oo# #:. x=-2# vertical asymptote We could looking for horizontal/slant asymptotes #lim_(x rarr +oo) f(x)=lim_(x rarr +oo)log(x+2)=+oo# #:.# no horizontal asymptotes the slant asymptote formula is #y=mx+q# with #m=lim_(x rarr +oo)f(x)/x# #q=lim_(x rarr +oo)[f(x)-mx]# #m=lim_(x rarr +oo)f(x)/x=lim_(x rarr +oo)log(x+2)/x=(+oo)/(+oo)# Applying The L'Hopital's rule #lim_(x rarr +oo)(h(x))/(i(x))=lim_(x rarr +oo)(h'(x))/(i'(x))# #lim_(x rarr +oo)log(x+2)/x=lim_(x rarr +oo)(1/(x+2))/1=# #m=lim_(x rarr +oo)1/(x+2)=0# #q=lim_(x rarr
+oo)[f(x)-mx]=lim_(x rarr +oo)[log(x+2)-0x]=# It is not finite, then #cancel(EE)# slant asymptote Does y log x have an asymptote?The domain of the graph y = log (x) is therefore (0, ∞) and the range of the graph is (-∞, ∞). The x-intercept is located at x = 1, there is no y-intercept, and there is a vertical asymptote at x = 0.
What is the vertical asymptote of y log x?The vertical asymptote occurs at x=0 .
What is the asymptote in a log equation?The vertical asymptote is (are) at the zero(s) of the argument and at points where the argument increases without bound (goes to ∞ ).
|
What is the equation of the asymptote of the graph of y log x?
Postagens relacionadas
direito autoral © 2024 cemle Inc.
