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AP Calculus AB

AP Calculus AB. Day 13 Section 3.9. Linear Approximation. Non-calculator application of the tangent line. Used to estimate values of f(x) at ‘difficult’ x-values. (ex: 1.03, 2.99, 7.01) Steps: a. Find the equation of the tangent line to f(x) at an ‘easy’ value nearby.

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AP Calculus AB

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  1. AP Calculus AB Day 13 Section 3.9 Perkins

  2. Linear Approximation Non-calculator application of the tangent line. Used to estimate values of f(x) at ‘difficult’ x-values. (ex: 1.03, 2.99, 7.01) Steps: a. Find the equation of the tangent line to f(x) at an ‘easy’ value nearby. b. Plug the ‘difficult’ x-value in to get a reasonable estimate of what the actual y-value will be.

  3. 1. Find the equation of the tangent line to f(x) at x = 1.

  4. 2. Use the equation of the tangent line to f(x) at x = 1 to estimate f(1.01). This estimate will be accurate as long as the x-value is very close to the point of tangency.

  5. AP Calculus AB Day 13 Section 3.9 Perkins

  6. Linear Approximation

  7. 1. Find the equation of the tangent line to f(x) at x = 1.

  8. 2. Use the equation of the tangent line to f(x) at x = 1 to estimate f(1.01).

  9. Finding Differentials To estimate a y-value using a differential: 1. Find a y-value at a nearby x-value. 2. Add the value of your differential. Differential Change in y. Change in x. Slope of tangent line at a given x. 3. Estimate f(0.03) without your calculator. 4. Estimate f(8.96) without your calculator.

  10. Finding Differentials 3. Estimate f(0.03) without your calculator. 4. Estimate f(8.96) without your calculator.

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