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Chapter 5: Problem 48
Find the derivative of the function. \(f(x)=\arcsin x+\arccos x\)
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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. $$ \int_{0}^{4} \sqrt{x} e^{x} d x $$
Use implicit differentiation to find an equation of the tangent line to the graph of the equation at the given point. \(\arctan (x+y)=y^{2}+\frac{\pi}{4}, \quad(1,0)\)
Horizontal Motion The position function of a particle moving along the \(x\) -axis is \(x(t)=A e^{k t}+B e^{-k t},\) where \(A, B,\) and \(k\) are positive constants. (a) During what times \(t\) is the particle closest to the origin? (b) Show that the acceleration of the particle is proportional to the position of the particle. What is the constant of proportionality?
Find an equation of the tangent line to the graph of the function at the given point. \(y=2 \arcsin x, \quad\left(\frac{1}{2}, \frac{\pi}{3}\right)\)
Find the derivative of the function. \(g(x)=\frac{\arcsin 3 x}{x}\)
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