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AP Calculus handout exercise on identifying outer and inner functions in integrals for substitution.

Table from an AP Calculus student handout titled "Inner and Outer Functions," showing five indefinite integrals where students must identify the outside function f(x) and inside function g(x) for each integral involving a composition of functions.

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Show Answer Key & Explanations Step-by-step solution for: Solved AP CALCULUS STUDENT HANDOUT Inner and Outer Functions ...

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1. $f(x) = \frac{1}{\sqrt{x}}$, $g(x) = x^2 + 5x + 1$
2. $f(x) = \frac{1}{x^3}$, $g(x) = 1 + \sqrt{x}$
3. $f(x) = x^{3/4}$, $g(x) = x^4 + 2x^2 + 7$
4. $f(x) = \frac{1}{\sqrt{x}}$, $g(x) = x + 4$
5. $f(x) = x^9$, $g(x) = x^2 + 1$

Parent Tip: Review the logic above to help your child master the concept of outer limits the ap calc worksheet.

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