Limits, L'Hopital's Rule and Integrals
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1. Evaluate 2)
2. Differentiate the function f(x) = ln(2x+3)
3. Find lim x∞ (e2x / (x + 5)3). Apply L'Hopital's rule as many time as necessary, verify your results after each application.
4. Evaluate ∫xsinh(x)dx
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Solution Summary
Limits, L'Hopital's Rule and Integrals are investigated.
Solution Preview
1. Int [ dt/(t+1)^2 ] Let (t+1) = x; hence, dt = dx
= Int [ dx/x^2 ] = -1/x
Now apply the limits; when t=1, x = 2 ; t=2, x=3
Hence, integral = 1/2 - 1/3 = 1/6
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2. f(x) = ln (2x+3)
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