evaluate the lim as x heads towards infinity of (sinhx)/ (e^x)
Nevermind I got the answer!
Oh wait I made a mistake..still need help! Thanks.
Is the answer 1/2?
To evaluate the limit of the function (sinh x)/(e^x) as x approaches infinity, we can use L'Hospital's Rule. L'Hospital's Rule states that if we have an indeterminate form "0/0" or "∞/∞", we can differentiate the numerator and the denominator separately until we obtain a determinate form.
Let's differentiate the numerator and denominator separately:
The derivative of sinh x with respect to x is cosh x.
The derivative of e^x with respect to x is e^x.
Now, let's rewrite the limit after taking the derivatives:
lim (x → ∞) (cosh x)/(e^x)
Next, let's analyze the new limit as x approaches infinity. The function e^x grows faster than cosh x as x becomes larger, so the numerator approaches infinity while the denominator grows even faster, also approaching infinity.
Therefore, the limit as x approaches infinity of (sinh x)/(e^x) is 0.