By examining the appropriate limits, ascertain the final behavior of the following transcendental functions. The associated graph is then simply sketched, with any asymptotes indicated.f(x)=2x

Question

2abehn · Accepted Answer

Step 1 To determine the end behavior of the following transcendental functions by analyzing appropriate limits. Given function is f(x)=2x To find end behavior of function f(x)=2x we have to find asymptotes for f(x)=2x 1) To find horizontal asymptotes: The line y=L is a horizontal asymptote of the function y=f(x) if either limx→∞f(x)=L or limx→−∞f(x)=L and L is finite. Now here, limx→∞2x=2∞=∞ and limx→−∞2x=2−∞=0 Therefore the line y=0 is the horizontal asymptote for f(x)=2x Step 2 2) To find vertical asymptotes: The line x=L is a vertical asymptote of the function f(x)=2x if the limit of the function at this point is infinite. Here the function f(x)=2x is defined for every value of x. Therefore there are no vertical asymptotes for f(x)=2x 3) To find slant asymptotes: The line y=mx+b is slant asymptote of a function y=f(x) if either m=limx→∞(f(x)x)=L or m=limx→−∞(f(x)x)=L and L is finite and zero m=limx→∞(f(x)x)=limx→∞2xx=∞ and m=limx→−∞(f(x)x)=limx→−∞2xx=0 Here the value of L is not finite and non zero. Therefore the function f(x)=2x has no slant asymptotes. Step 3 The sketch of the graph of function f(x)=2x is,

Determine the end behavior of the following transcendental functions by

Answered question

Answer & Explanation

New Questions in Calculus 1