Textbook Question
Evaluate the integrals in Exercises 53–76.
63. ∫(from -1 to -√2/2)dy/(y√(4y²-1))
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Evaluate the integrals in Exercises 53–76.
63. ∫(from -1 to -√2/2)dy/(y√(4y²-1))
Use l’Hôpital’s rule to find the limits in Exercises 7–52.
32. lim (x → 0) (3^x - 1) / (2^x - 1)
In Exercises 7–10, determine from its graph if the function is one-to-one.
f(x) = 3 - x, x < 0
= 3, x ≥ 0
In Exercises 59–86, find the derivative of y with respect to the given independent variable.
59. y = 2^x
133. Find the absolute maximum value of
f(x) = x^2 * ln(1/x)
and say where it is assumed.
Solve the differential equation in Exercises 9–22.
15. √x (dy/dx) = e^(y+√x), x > 0