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Sketch the graph of the given function. Check your sketch using technology. g(t) = e-t2 (a) Indicate the t- and y-intercepts. (If an answer does not exist, enter DNE.) t-intercept (t, y) = y-intercept (t, y) = (b) Indicate any extrema. (If an answer does not exist, enter DNE.) -Select-- (t, y) = | (c) Indicate any points of inflection. (Order your answers from smallest to largest t. If an answer does not exist, enter DNE.) (t, y) = (t, y)

Sketch the graph of the given function. Check your sketch using technology. g(t) = e-t2 (a) Indicate the t- and y-intercepts. (If an answer does not exist, enter DNE.) t-intercept (t, y) = y-intercept (t, y) = (b) Indicate any extrema. (If an answer does not exist, enter DNE.) -Select-- (t, y) = | (c) Indicate any points of inflection. (Order your answers from smallest to largest t. If an answer does not exist, enter DNE.) (t, y) = (t, y)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Sketch the Graph of the Given Function** Consider the function: \[ g(t) = e^{-t^2} \] **Instructions:** 1. Sketch the graph of the given function. Use technology to verify your sketch. **(a) Indicate the \( t \)- and \( y \)-intercepts.** - If an answer does not exist, enter DNE (Does Not Exist). - \( t \)-intercept \((t, y) = (\) [input box] \()\) - \( y \)-intercept \((t, y) = (\) [input box] \()\) **(b) Indicate any extrema.** - If an answer does not exist, enter DNE. - [Dropdown to select minimum or maximum] \((t, y) = (\) [input box] \()\) **(c) Indicate any points of inflection.** - Order your answers from smallest to largest \( t \). If an answer does not exist, enter DNE. - \((t, y) = (\) [input box] \()\) - \((t, y) = (\) [input box] \()\)
Transcribed Image Text:**Sketch the Graph of the Given Function** Consider the function: \[ g(t) = e^{-t^2} \] **Instructions:** 1. Sketch the graph of the given function. Use technology to verify your sketch. **(a) Indicate the \( t \)- and \( y \)-intercepts.** - If an answer does not exist, enter DNE (Does Not Exist). - \( t \)-intercept \((t, y) = (\) [input box] \()\) - \( y \)-intercept \((t, y) = (\) [input box] \()\) **(b) Indicate any extrema.** - If an answer does not exist, enter DNE. - [Dropdown to select minimum or maximum] \((t, y) = (\) [input box] \()\) **(c) Indicate any points of inflection.** - Order your answers from smallest to largest \( t \). If an answer does not exist, enter DNE. - \((t, y) = (\) [input box] \()\) - \((t, y) = (\) [input box] \()\)
(d) Indicate the behavior near singular points of \( f \). - \( \circ \) \( y \to +\infty \) as \( t \to 0 \) - \( \circ \) \( y \to 0 \) as \( t \to 0 \) - \( \circ \) \( y \to -\infty \) as \( t \to 0 \) - \( \circ \) \( y \to 1 \) as \( t \to 0 \) - \( \circ \) The function is defined everywhere on the domain. (e) Indicate the behavior at infinity. - \( \circ \) \( y \to -\infty \) as \( t \to \pm\infty \) - \( \circ \) \( y \to +\infty \) as \( t \to -\infty \); \( y \to -\infty \) as \( t \to +\infty \) - \( \circ \) \( y \to +\infty \) as \( t \to \pm\infty \) - \( \circ \) \( y \to -\infty \) as \( t \to -\infty \); \( y \to +\infty \) as \( t \to +\infty \) - \( \circ \) \( y \to 0 \) as \( t \to \pm\infty \)
Transcribed Image Text:(d) Indicate the behavior near singular points of \( f \). - \( \circ \) \( y \to +\infty \) as \( t \to 0 \) - \( \circ \) \( y \to 0 \) as \( t \to 0 \) - \( \circ \) \( y \to -\infty \) as \( t \to 0 \) - \( \circ \) \( y \to 1 \) as \( t \to 0 \) - \( \circ \) The function is defined everywhere on the domain. (e) Indicate the behavior at infinity. - \( \circ \) \( y \to -\infty \) as \( t \to \pm\infty \) - \( \circ \) \( y \to +\infty \) as \( t \to -\infty \); \( y \to -\infty \) as \( t \to +\infty \) - \( \circ \) \( y \to +\infty \) as \( t \to \pm\infty \) - \( \circ \) \( y \to -\infty \) as \( t \to -\infty \); \( y \to +\infty \) as \( t \to +\infty \) - \( \circ \) \( y \to 0 \) as \( t \to \pm\infty \)
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