CALCULUS I TEST #2 |

**Time limit:**

- 2 hours

**Instructions:**

- No graphing calculators

No notes or crib sheets allowed

Show all work. Write neatly and big enough to see!!

Numbers in parentheses ( ) are mark values.

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A/ Find y '. Do not simplify beyond basic algebra.

1) y = x^{ 5/3} sin 2x |
2) | 3) x sin y = y cos x |

4) y = (2 cos 5x - 4 tan 3x)^{7} |
5) y = 3 sin^{2} 4x - 2 cos^{ 3} x^{2} |

(15)

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B/ 1) Write the equation of the tangent to the curve *x ^{ 2 }y + 3xy^{ 2} - 2y^{ 3} + 2 = 0* at

(4)

2) Evaluate the limits:

a) | b) |

(4)

3) Find *c* such that *c **Î** (0, 4)* and *c* satisfies the hypothesis of the

**Mean Value Theorem** for *f(x) = x ^{2} + 3x +1*.

(4)

4) Using differentials, approximate the change in the area of a circle

if the **radius changes from 2 inches to 1.96 inches**. (A = o r^{ 2})

(4)

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C/

1) One leg of a right triangle increases at **3 in./sec** while the other increases at **2 in./sec**.

Find the rate at which the hypotenuse is changing when the first leg is **6 inches**

and the 2nd leg is **8 inches**. (draw a diagram!)

(4)

2) Find the area of the largest rectangle having two vertices on the *x-axis* and

two vertices above the *x-axis* on the curve *y = 9 - x ^{ 2}*.(draw a diagram!)

(5)

3) Draw the graph of and list the M2I2ACIDS & any other important features for

** Clearly indicate *f '(x), f "(x)* and how you found the asymptotes.

(hint: factor the demominator)

(10)

TOTAL (50)

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Back to Calculus I MathRoom Index

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*(all content of the MathRoom Lessons **© Tammy the Tutor; 2002 - 2005).*

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**M _{2 }I_{2 }ACIDS** stands for:

**M**aximum, **M**inimum, **I**ntercepts, **I**nflection points, **A**symptotes,

**C**oncavity, **I**ncreasing intervals, **D**ecreasing intervals and **S**ymmetry.

For notes on this topic see lesson on curve sketching.