Test 1

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Question

Test 1

1. Differentiate the function.

y = \ln (x^{5} \sin^{2} x)

2.Evaluate the integral

\int_{0}^{2} \frac{e^{x}}{1 + e^{2 x}} d x

3. Find the exact value of each expression

\ln e^{π}

and b.

\tan (a r c \sin \frac{1}{2})

4. Find the values of for

λ

which

y = e^{λ x}

satisfies the equation

7 y + 7 y ‘ = y ‘ ‘

5. Use the properties of logarithms to expand the quantity.

\log_{2} (\frac{x^{10} y}{z^{5}})

6. Differentiate the function

y = \frac{\ln x}{5 + x}

7. Use logarithmic differentiation to find the derivative of the function.

y = {(x + 2)}^{7 / x}

8. Evaluate the integral.

\int \tan (x) \ln (\cos x) d x

9. Evaluate the integral.

\int \frac{c s c^{2} (x)}{1 + c o t x} d x

10. Evaluate the integral.

\int_{0}^{4} \frac{1}{16 + x^{2}} d x

11. Evaluate the integral.

\int \sin h (m x) d x

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This question is taken from Math 266 – Cal/Analytic Geometry 2 » Spring 2022 » Tests

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