Chapter 5: Problem 13
Use a calculator to approximate the value. Round your answer to two decimal places. \(\operatorname{arcsec} 1.269\)
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Chapter 5: Problem 13
Use a calculator to approximate the value. Round your answer to two decimal places. \(\operatorname{arcsec} 1.269\)
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Use a computer algebra system to find the linear approximation \(P_{1}(x)=f(a)+f^{\prime}(a)(x-a)\) and the quadratic approximation \(P_{2}(x)=f(a)+f^{\prime}(a)(x-a)+\frac{1}{2} f^{\prime \prime}(a)(x-a)^{2}\) of the function \(f\) at \(x=a\) . Sketch the graph of the function and its linear and quadratic approximations. \(f(x)=\arccos x, \quad a=0\)
In Exercises 106–108, verify the differentiation formula. $$ \frac{d}{d x}\left[\operatorname{sech}^{-1} x\right]=\frac{-1}{x \sqrt{1-x^{2}}} $$
Explain why the domains of the trigonometric functions are restricted when finding the inverse trigonometric functions.
Find the derivative of the function. \(y=\ln \left(t^{2}+4\right)-\frac{1}{2} \arctan \frac{t}{2}\)
Find the derivative of the function. \(f(x)=\arcsin x+\arccos x\)
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