Textbook Question
126. Show that the sum arctan(x)+arctan(1/x) is constant.
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126. Show that the sum arctan(x)+arctan(1/x) is constant.
Evaluate the integrals in Exercises 33–54.
∫(e^(3x) + 5e^(-x)) dx
Evaluate the integrals in Exercises 33–54.
∫ (e^(1/x) / x²) dx
For problems 49–52 use implicit differentiation to find dy/dx at the given point P.
49. 3arctan(x) + arcsin(y) = π/4; P(1, -1)
Evaluate the integrals in Exercises 53–76.
73. ∫(from 0 to ln√3) e^x dx/(1+e^(2x))
Use l’Hôpital’s rule to find the limits in Exercises 7–52.
9. lim (t → -3) (t³ - 4t + 15) / (t² - t - 12)