Determine the following limits.

lim x→−...

Question

Determine the following limits.

lim x→−∞ (e^x cos x +3)

Accepted Answer

Welcome back, everyone. Evaluate the limit as X approaches negative infinity for the function F of X equals E to the power of X X + 7. Were given 4 answer choices A says 0, B 7 C 7, and D does not exist. So let's write the limit limit as x approaches negative infinity, and the given function is E to the power of X multiplied by sin x + 7. What we're going to do is basically apply the properties of limits. We can rewrite this as limit, as X approaches negative infinity of E to the power of X. Multiplied by sin x. Plus limit. When x approaches negative infinity of 7. Now let's analyze the first limit. We have a product of two functions as X approaches negative infinity. We can say that we want to evaluate the limit as X approaches negative infinity of EX. Right? And basically, if we apply the right substitution, this is going to be equal to each, the power of negative infinity, we can rewrite that. As one divided by each, the power of infinity. Which is basically 1 divided by infinity and 1 divided by infinity is approaching 0. So the limit is going to be equal to 0, and sin X, when X approaches negative infinity is basically oscillating between -1 and 1, right, if we visualize the graph of sine. So essentially we have a finite number. Multiplied by 0, which gives us 0. So the first limit is going to be equal to 0, and the second limit. is a constant, right? So it's independent of X, meaning it's simply equal to 7. It is equal to the given constant term, and therefore, if we get 0 + 7, we end up with our final result, which is option C7. Thank you for watching.

Determine the following limits.

lim x→−∞ (e^x cos x +3)

Key Concepts

Limits at Infinity

Exponential Functions

Trigonometric Functions

Watch next