2.14 Linear Approximations: Quiz

Problem 3

Consider the function f(x) = e^x. Let x = 0, dx = Δx = 0.5. Sketch the curve and the tangent line at x = 1 as in section 2.14 of the textbook, and give the equation of the tangent line. What are dy and Δy?

Answers, problem 3

The tangent line (drawn in pink) is T(x) = 1 + x. dy is T(1.5) − T(1) = 0.5. Δy is e^1.5 - e¹ ≈ 1.763.

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