Find an equation of the tangent line to y = x ? e 0.1 x at the location x = 3.5.

Question

Find an equation of the tangent line to y = x?e0.1x at the location x = 3.5. You can use decimals in the equation of the tangent line, but you should keep at least 4 decimal places of accuracy until you finish the entire problem. You can also use exact methods, but you have to convert your answers to decimals before you enter them. Required Graphing Exercise: Graph the function and the tangent line on one set of axes with domain ?8 ? x ? 8. Then answer the remaining questions. What is the slope of the tangent line? Be accurate to three decimal places.
Find the y-intercept of the tangent line, accurate to three decimal places. y =
Find the x-intercept of the tangent line, accurate to three decimal places. x =
Find the acute angle between the tangent line and the x-axis. Write your answer indegrees with one decimal place of accuracy. degrees Find the acute angle between the tangent line and the y-axis. Write your answer indegrees with one decimal place of accuracy.
degrees Find an equation of the tangent line to y = x?e0.1x at the location x = 3.5. You can use decimals in the equation of the tangent line, but you should keep at least 4 decimal places of accuracy until you finish the entire problem. You can also use exact methods, but you have to convert your answers to decimals before you enter them. y = x?e0.1x Required Graphing Exercise: Graph the function and the tangent line on one set of axes with domain ?8 ? x ? 8. Then answer the remaining questions. ?8 ? x ? 8. What is the slope of the tangent line? Be accurate to three decimal places.
Find the y-intercept of the tangent line, accurate to three decimal places. y =
y =
Find the x-intercept of the tangent line, accurate to three decimal places. x =
x =
Find the acute angle between the tangent line and the x-axis. Write your answer indegrees with one decimal place of accuracy. degrees Find the acute angle between the tangent line and the y-axis. Write your answer indegrees with one decimal place of accuracy.
degrees

Explanation / Answer

Acute angle:                tan^-1(1.916) = 62.4

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