5 Steps to a 5: AP Calculus BC 2022 by William Ma

Author:William Ma
Language: eng
Format: epub
Publisher: McGraw-Hill Education
Published: 2021-08-15T00:00:00+00:00

Estimating the nth Root of a Number

Another way of expressing the tangent line approximation is: f (a + Δ x) ≈ f(a) + f′(a)Δ x, where Δ x is a relatively small value.

Example 1

Find the approximation value of using linear approximation.

Using f (a + Δ x) ≈ f (a) + f′(a)Δ x, let ; a = 49 and Δ x = 1.

Thus,

Example 2

Find the approximate value of using linear approximation.

Let f(x) = x1/3, a = 64, Δx = −2. Since and , you can use f(a + Δx) ≈ f(a) + f′(a)Δx. Thus, .

• Use calculus notations and not calculator syntax, e.g., write ∫x2dx and not ∫(x∧2, x).

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