Thomas Calculus

TARGET DECK Mathematics::Thomas Calculus

Problem 7.1.50::$3$

Problem 7.1.51::$\frac{1}{9}{x}^{-2/3}$

Problem 7.1.52::$-\frac{1}{6}(1-x{)}^{-2/3}$

Problem 7.1.53::$-\frac{1}{3}{x}^{-2/3}$

Problem 7.1.54::$x^{5/3}$

Problem 7.2.68::$y^{\prime }=\left(\frac{5}{x+1}-\frac{5}{2x+1}\right)y$

Problem 7.2.69::$y^{\prime }=\frac{1}{3}\left(\frac{1}{x}+\frac{1}{x-2}-\frac{2x}{x^2+1}\right)y$

Problem 7.2.70::$y^{\prime }=\frac{1}{3}\left(\frac{1}{x}+\frac{1}{x+1}+\frac{1}{x-2}-\frac{2x}{x^2+1}-\frac{2}{2x+3}\right)y$

Problem 7.3.115::$y^{\prime }=\left(\frac{x}{x+1}+\ln (x+1)\right)y$

Problem 7.3.116::$y^{\prime }=\left(\frac{2}{x}+2+2\ln x\right)y$

Problem 7.3.117::$y^{\prime }=\left(\frac{1}{2}+\frac{1}{2}\ln t\right)y$

Problem 7.3.118::$y^{\prime }=\frac{\ln t+2\sqrt{t}}{2\sqrt{t}}$

Problem 7.3.119::$y^{\prime }=(\ln \sin x+x\cot x)y$

Problem 7.3.120::$y^{\prime }=\left(\cos x\ln x+\frac{\sin x}{x}\right)y$

Problem 7.3.121::$y^{\prime }=\cos x^x(1+\ln x)x^x$

Problem 7.3.122::$y^{\prime }=\frac{\ln \ln x+1}{x}y$

Problem 7.3.123::$y^{\prime }=\left(\frac{3}{(x-1{)}^2}\ln x+\frac{3}{x(x-1)}\right)y$

Problem 7.3.125::$y^{\prime }=\frac{1-\ln x}{x^2(\ln y+1)}$

Problem 7.3.127::$f(x)=(1+\ln x{)}^2$

Problem 7.3.128::$f(x)=e^{x+1}$

Problem 8.8.1::$\frac{\pi }{2}$

Problem 8.8.13::$0$

Problem 8.8.15::$\sqrt{3}$

Problem 8.8.17::$\pi$

Problem 8.8.19::$\ln \left(1+\frac{\pi }{2}\right)$

Problem 8.8.21::$-1$

Problem 8.8.23::1

Problem 8.8.25::$-\frac{1}{4}$

Problem 8.8.27::$\frac{\pi }{2}$

Problem 8.8.70::

Problem 9.7.8::(a)$-3<x<-1$
(b)$-3<x<-1$
(c)$x=-1$