Calculus II Quiz 1 Feb. 26, 2009 Name: Student ID number: 1. (10 pts; 2 pts for each problem) Find the derivative of the given function. † For x > 0, f (x) = ln x, f

Calculus II Quiz 1 Feb. 26, 2009

Name: Student ID number:

1. (10 pts; 2 pts for each problem) Find the derivative of the given function.

• For x > 0, f(x) = ln x, f⁰(x) = .

• f(x) = 3x^1/3, f⁰(x)x = .

• f(x) = e^x+ x, f⁰(x)x = .

• f(x) = cos x, f⁰(x) = .

• For x 6= 0, f(x) = x²+ 1

x , f⁰(x) = .

2. (10 pts; 2 pts for each problem) Find the general antiderivative of the given function (f (x) = F⁰(x)).

• For x 6= 0, f(x) = 1

x, F (x) = +C

• f(x) = 3x^1/3, F (x) = +C

• f(x) = e^x+ x, F (x) = +C

• f(x) = cos x, F (x) = +C

• For x 6= 0, f(x) = x²+ 1

x , F (x) = +C

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Name: Student ID number:

3. (10 pts) Find the derivative of

∫ x³ x²

tan t dt

4. The equation 7x²y³−5xy²−4y = 7 defines y implicitly as a function of x. Find dy

dx.

5. Find the derivative of x^2x

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Name: Student ID number:

6. (10 pts) Compute lim

x→∞

2x− 1 e^x

7. Evaluate the given integral

∫ 4 1

e^√x

√xdx

8. Evaluate the given integral

∫ 5x

x²− 3x − 4dx

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Name: Student ID number:

9. Determine whether the integral converges or diverges,

•

∫ _∞

−∞

x³dx

• lim

R→∞

∫ _R

−R

x³dx

10. Evaluate the given integral

∫ 1 0

x^−1/3dx

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