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The functions F(x) and G(r) are given by F(x) = arctant dt and G(2)=√ earctant dt Note: Like the function et, the integrands used to define both F(x) and G(z) are not possible to anti-differentiate in terms of our old, familiar functions, so don't waste your precious time trying. A) (F We can express the function G(z) as a composition of F(r) with another function; that is, we can write G(x) = F(h(z)). Identify the "inside function" h(x). B) Find F'(x) and G'(x). Check that L'Hopital's rule applies to the limits F(x) lim 1-0 I 6 and use this rule to evaluate these limits. and lim G(x) 1-0 ²

The functions F(x) and G(r) are given by F(x) = arctant dt and G(2)=√ earctant dt Note: Like the function et, the integrands used to define both F(x) and G(z) are not possible to anti-differentiate in terms of our old, familiar functions, so don't waste your precious time trying. A) (F We can express the function G(z) as a composition of F(r) with another function; that is, we can write G(x) = F(h(z)). Identify the "inside function" h(x). B) Find F'(x) and G'(x). Check that L'Hopital's rule applies to the limits F(x) lim 1-0 I 6 and use this rule to evaluate these limits. and lim G(x) 1-0 ²

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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may you please explain how i can evaluate this without a calculator

The functions F(x) and G(r) are given by F(x) = arctant dt and G(2)=√ earctant dt Note: Like the function et, the integrands used to define both F(x) and G(z) are not possible to anti-differentiate in terms of our old, familiar functions, so don't waste your precious time trying. A) (F We can express the function G(z) as a composition of F(r) with another function; that is, we can write G(x) = F(h(z)). Identify the "inside function" h(x). B) Find F'(x) and G'(x). Check that L'Hopital's rule applies to the limits F(x) lim 1-0 I 6 and use this rule to evaluate these limits. and lim G(x) 1-0 ²
Transcribed Image Text:The functions F(x) and G(r) are given by F(x) = arctant dt and G(2)=√ earctant dt Note: Like the function et, the integrands used to define both F(x) and G(z) are not possible to anti-differentiate in terms of our old, familiar functions, so don't waste your precious time trying. A) (F We can express the function G(z) as a composition of F(r) with another function; that is, we can write G(x) = F(h(z)). Identify the "inside function" h(x). B) Find F'(x) and G'(x). Check that L'Hopital's rule applies to the limits F(x) lim 1-0 I 6 and use this rule to evaluate these limits. and lim G(x) 1-0 ²
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