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Fri Sep 20 16:14
chem 040 - Google Docs
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Mathway | Calculus Problem
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Let $J(x)$ nave the ronowing grapn:
(a) Compute the limit $\lim _{x \rightarrow 0.7} x f(x)$.
(b) Compute $\lim _{x \rightarrow 2.5} x^{2} f(x)$. How does this compare to the function $g(x)=x f(x)$ evaluated at $x=2.5$ ?
(c) Does the limit $\lim _{z \rightarrow 1.5} \frac{f(x)}{x-1.5}$ exist? Explain why or why not.
B. Please select file(s) $\square$

Q: Chrome File Edit View History Bookmarks Profiles Tab Window Help A 64\% Fri Sep 20 16:14 chem 040 - Google Docs Manage writing suggestions Submit Homework (Week 3) Mathway | Calculus Problem New Tab gradescope.com/courses/849437/assignments/4968588/submissions/new Relaunch to update All Bookmarks 0/3 Questions Answered View fullscreen Let $J(x)$ nave the ronowing grapn: (a) Compute the limit $\lim _{x \rightarrow 0.7} x f(x)$. (b) Compute $\lim _{x \rightarrow 2.5} x^{2} f(x)$. How does this compare to the function $g(x)=x f(x)$ evaluated at $x=2.5$ ? (c) Does the limit $\lim _{z \rightarrow 1.5} \frac{f(x)}{x-1.5}$ exist? Explain why or why not. B. Please select file(s) $\square$

∻Solution by Steps∻ ‖ step 1 ⋮ To compute the limit as $ x $ approaches $ 0.7 $ of $ x f(x) $, we evaluate $ \lim_{x \to 0.7} x f(x) $. The value of $ f(0.7) $ can be determined from the graph. ‖ ‖ step 2 ⋮ For the limit $ \lim_{x \to 2.5} x^2 f(x) $, we find $ f(2.5) $ from the graph and then compute $ 2.5^2 f(2.5) $. This will give us the value of the limit. ‖ ‖ step 3 ⋮ To compare this with $ g(x) = x f(x) $ evaluated at $ x = 2.5 $, we calculate $ g(2.5) = 2.5 f(2.5) $ and compare the two results. ‖ ‖ step 4 ⋮ For the limit $ \lim_{x \to 1.5} \frac{f(x)}{x - 1.5} $, we need to check if $ f(x) $ approaches $ 0 $ as $ x $ approaches $ 1.5 $. If $ f(1.5) = 0 $, then the limit exists; otherwise, it does not. ‖ ∻Answer∻ ⚹ The limits and comparisons will depend on the specific values of $ f(x) $ at the points of interest from the graph. ⚹ ∻Key Concept∻ ⚹ Understanding limits and their evaluation using graphical information is crucial in calculus. ⚹ ∻Explanation∻ ⚹ The limits help us understand the behavior of functions at specific points, and comparing different functions at those points provides insight into their relationships. ⚹◊What is the general approach to determine the limit of a function as $ x $ approaches a specific value?⍭ Generate me a similar question◊

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∻Solution by Steps∻ ‖ step 1 ⋮ To compute the limit as $ x $ approaches $ 0.7 $ of $ x f(x) $, we evaluate $ \lim_{x \to 0.7} x f(x) $. The value of $ f(0.7) $ can be determined from the graph. ‖ ‖ step 2 ⋮ For the limit $ \lim_{x \to 2.5} x^2 f(x) $, we find $ f(2.5) $ from the graph and then compute $ 2.5^2 f(2.5) $. This will give us the value of the limit. ‖ ‖ step 3 ⋮ To compare this with $ g(x) = x f(x) $ evaluated at $ x = 2.5 $, we calculate $ g(2.5) = 2.5 f(2.5) $ and compare the two results. ‖ ‖ step 4 ⋮ For the limit $ \lim_{x \to 1.5} \frac{f(x)}{x - 1.5} $, we need to check if $ f(x) $ approaches $ 0 $ as $ x $ approaches $ 1.5 $. If $ f(1.5) = 0 $, then the limit exists; otherwise, it does not. ‖ ∻Answer∻ ⚹ The limits and comparisons will depend on the specific values of $ f(x) $ at the points of interest from the graph. ⚹ ∻Key Concept∻ ⚹ Understanding limits and their evaluation using graphical information is crucial in calculus. ⚹ ∻Explanation∻ ⚹ The limits help us understand the behavior of functions at specific points, and comparing different functions at those points provides insight into their relationships. ⚹◊What is the general approach to determine the limit of a function as $ x $ approaches a specific value?⍭ Generate me a similar question◊

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