题目

MATH 2A LEC A: CALCULU... Midterm

多项填空题

The graphs of ff and gg are given below. Use them to evaluate each limit, if it exists. (If an answer does not exist, enter DNE.) (a) limx→2[f(x)+g(x)]=\lim_{x\rightarrow 2}[f(x)+g(x)]=[Fill in the blank], (b) limx→1[f(x)+g(x)]=\lim_{x \to 1} [f(x) + g(x)] =[Fill in the blank], (c) limx→0[f(x)g(x)]=\lim_{x \to 0} [f(x)g(x)] =[Fill in the blank], (d) limx→−1g(x)f(x)=\lim_{x \to -1} \frac{g(x)}{f(x)} =[Fill in the blank], (e) limx→2[x3f(x)]=\lim_{x \to 2} \left[x^3 f(x)\right] =[Fill in the blank], (f) limx→13+f(x)=\lim_{x \to 1} \sqrt{3 + f(x)} =[Fill in the blank],

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标准答案

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思路分析

We are asked to evaluate six limits using the graphs of f and g. Each item (a) through (f) corresponds to a manipulation of f(x) and g(x) as x approaches a certain value. In the absence of the actual graphs in this prompt, we rely on the provided correct values to guide the explanation and illustrate how these results typically arise from graph behavior. (a) lim_{x→2} [f(x) + g(x)] This limit is the sum of the individual limits, provided both limits exist. If f(x) → Lf and g(x) → Lg as x → 2, then f(x) + g(x) → Lf + Lg. The reported value is 3, so the combination of the left/right or approaching values of f and g at x = 2 yields a total of 3. Potential missteps could......Login to view full explanation