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Chapter 5: Problem 11
Use a calculator to approximate the value. Round your answer to two decimal places. \(\arccos (-0.8)\)
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In Exercises 83鈥�86, evaluate the definite integral using the formulas from Theorem 5.20. $$ \int_{0}^{1} \frac{1}{\sqrt{25 x^{2}+1}} d x $$
(a) Use a graphing utility to evaluate arcsin (arcsin 0.5) and \(\arcsin (\arcsin 1) .\) (b) Let \(f(x)=\arcsin (\arcsin x)\) Find the values of \(x\) in the interval \(-1 \leq x \leq 1\) such that \(f(x)\) is a real number.
Numerical Integration In Exercises 129 and 130 , approximate the integral using the Midpoint Rule, the Trapezoidal Rule, and Simpson's Rule with \(n=12 .\) Use a graphing utility to verify your results. $$ \int_{0}^{4} \sqrt{x} e^{x} d x $$
Find the derivative of the function. \(y=25 \arcsin \frac{x}{5}-x \sqrt{25-x^{2}}\)
Find an equation of the tangent line to the graph of the function at the given point. \(y=3 x \arcsin x, \quad\left(\frac{1}{2}, \frac{\pi}{4}\right)\)
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