Give the function f ( x ) = x 2 − 1 Sketch the graph of the function. Use the graph to state the domain and the range of the function. Find δ such that if 0 < | x − 2 | < δ , then | f ( x ) − 3 | < 0.2.
Give the function f ( x ) = x 2 − 1 Sketch the graph of the function. Use the graph to state the domain and the range of the function. Find δ such that if 0 < | x − 2 | < δ , then | f ( x ) − 3 | < 0.2.
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 57SE: Repeat the previous exercise to find the formula forthe APY of an account that compounds daily....
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- Give the function f ( x ) = x 2 − 1
- Sketch the graph of the function. Use the graph to state the domain and the range of the function.
- Find δ such that if 0 < | x − 2 | < δ , then | f ( x ) − 3 | < 0.2.
- Given the function: f ( x ) = (1 − cos x) / x2
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- Find the domain of f.
- Use a graphing utility to graph f. Is the domain of f obvious from the graph? If not, please explain.
- Use the graph to approximate lim x ⟶ 0 f ( x )
- Confirm your answer to part (c) analytically.
-
- Given the function f ( x ) = 1 /(x + 3) . Find lim Δx ⟶ 0 (f ( x + Δx ) − f ( x ))/ Δx
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