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Answer :
The limit lim _{x → c}[f(x) + 2g(x) - h(x)] is equal to -8.
To evaluate the limit lim _{x → c}[f(x) + 2g(x) - h(x)], we can use the given information about the limits of f(x), g(x), and h(x). Let's break down the expression step-by-step:
1. Start by substituting the given limits into the expression:
lim _{x → c}[f(x) + 2g(x) - h(x)] = lim _{x → c}[f(x)] + 2 * lim _{x → c}[g(x)] - lim _{x → c}[h(x)]
2. Substitute the given values:
= 2 + 2 * (-3) - 4
3. Simplify the expression:
= 2 - 6 - 4
= -8
Therefore, the limit lim _{x → c}[f(x) + 2g(x) - h(x)] is equal to -8.
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Based on the information given, the limit of f(x) as x approaches c is 2.
To evaluate the given limit, we can use the properties of limits. Let's call the function in question "f(x)".
The limit we are evaluating is written as:
lim_{x → c} [f(x)]
We are given that lim_{x → c} [f(x)] = 2, which means that as x approaches c, the function f(x) approaches 2.
Since we are not given any specific function or value for c, we cannot determine the exact value of the limit.
However, based on the information provided, we can conclude that the limit of f(x) as x approaches c is equal to 2.
In general, when evaluating limits, it is important to consider the properties of the functions involved, such as continuity and differentiability. These properties can help us determine the behavior of the function as it approaches a certain value.
In this case, we are only given the values of the limits for three functions: f(x), g(x), and h(x). The given values for these limits are not directly relevant to evaluating the limit of f(x) as x approaches c.
In conclusion, based on the information given, the limit of f(x) as x approaches c is 2. Please note that the specific value of c and the function f(x) are not provided, so we cannot determine the exact value of the limit.
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