Determine the end behavior of the following transcendental functions by analyzing appropriate limits. Then provide a simple sketch of the associated graph, showing asymptotes if they exist. f(x)=50e2x

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Determine the end behavior of the following transcendental functions by analyzing appropriate limits. Then provide a simple sketch of the associated graph, showing asymptotes if they exist.  f(x)=50e2x

komunidadO · Accepted Answer

Step 1 Here , find function limits at infinity for horizontal asymptotes, and find possible vertical asymptotes at points for which our function is not defined . limx→∞f(x)=limx→∞50e2x substitute for x =limx→∞50e∞ compute limit and simplify =0 limx→−∞f(x)=limx→−∞50e2x =50limx→−∞1e2x =50limx→−∞e−2x =50(∞) =∞ We have horizontal asymptote at y=0 Step 2 We have no vertical asymptotes because our function is defined for every x Now, check for slant asymptotes. Using formula limx→±∞f(x)x=k where k represents slope of our line (slant asymptotes) limx→∞50e2xx =limx→∞50xe2x =0 As our slope is zero , there is no slant asymptotes. graph :

Determine the end behavior of the following transcendental functions by

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