Question

Evaluate the following limit: lim(x → 0) [cos(x) + e^x + 3x₂]

Answer 1

The limit of the expression as x approaches 0 is found by evaluating the limit of each term separately and summing their values, resulting in a limit of 2.

Step-by-step explanation:

The question asks to evaluate the following limit: lim(x → 0) [cos(x) + e^x + 3x²].

To find this limit, we consider each term separately as x approaches zero:

• The limit of cos(x) as x approaches 0 is cos(0), which equals 1.
• The limit of e^x as x approaches 0 is e^0, which equals 1.
• The limit of 3x² as x approaches 0 is 0, because any real number squared and multiplied by a constant will approach 0 as the number itself approaches 0.

Adding these results together, the limit of the entire expression as x approaches 0 is 1 + 1 + 0 = 2.