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5:02Approximation Error
In Exercises 29–34, each function f(x) changes value when x changes from x₀ to x₀ + dx. Find
a. the change Δf = f(x₀ + dx) − f(x₀);
b. the value of the estimate df = fʹ(x₀) dx; and
c. the approximation error |Δf − df|.
f(x) = x⁻¹, x₀ = 0.5, dx = 0.1
In Exercises 43–50, find by implicit differentiation.
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√xy = 1
Find the derivatives of the functions in Exercises 1–42.
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𝔂 = ( √ x )²
( 1 + x )
Show that the line y = mx + b is its own tangent line at any point (x₀, mx₀ + b).
In Exercises 83–88, find equations for the lines that are tangent, and the lines that are normal, to the curve at the given point.
(y - x)² = 2x + 4, (6, 2)
Normal lines to a parabola Show that if it is possible to draw three normal lines from the point (a, 0) to the parabola x = y² shown in the accompanying diagram, then a must be greater than 1/2. One of the normal lines is the x-axis. For what value of a are the other two normal lines perpendicular?
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