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Prove that $1 + rac{x^2}{ ext{cos } x} = 1 + O(x^4)$ as $x$ approaches 0.
Prove that $1 + rac{x^2}{ ext{cos } x} = 1 + O(x^4)$ as $x$ approaches 0.
Yes
Express the sequence $x_n = rac{3n^2 + 4n}{n^2 + 1}$ as $L + O(z^n)$.
Express the sequence $x_n = rac{3n^2 + 4n}{n^2 + 1}$ as $L + O(z^n)$.
Yes
Prove that the function $f(x) = x^3 + 4x^2 - 10$ has a root in the interval $[1, 2]$.
Prove that the function $f(x) = x^3 + 4x^2 - 10$ has a root in the interval $[1, 2]$.
Yes
Determine the number of bisection iterations that guarantee an approximation correct within 6 decimal places for a function $f$ in the interval $[3, 5]$ with a unique root.
Determine the number of bisection iterations that guarantee an approximation correct within 6 decimal places for a function $f$ in the interval $[3, 5]$ with a unique root.
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Verify that the function $g(x) = rac{4}{4+x}$ has a unique fixed point in the interval $[1, 2]$.
Verify that the function $g(x) = rac{4}{4+x}$ has a unique fixed point in the interval $[1, 2]$.
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