Textbook Question
Solve the differential equation in Exercises 9–22.
21. (1/x)(dy/dx) = ye^(x²) + 2√y e^(x²)
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Solve the differential equation in Exercises 9–22.
21. (1/x)(dy/dx) = ye^(x²) + 2√y e^(x²)
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
Evaluate the integrals in Exercises 33–54.
∫₀^(π/4) (1 + e^(tan θ)) sec²θ dθ
Use l’Hôpital’s rule to find the limits in Exercises 7–52.
41. lim (x → 0⁺) (ln x)² / ln(sin x)
In Exercises 59–86, find the derivative of y with respect to the given independent variable.
65. y = (cos θ)^(√2)