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 sin2 4x - 2 cos 3 x2

(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 P(1, 2).

(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) = x2 + 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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(all content of the MathRoom Lessons © Tammy the Tutor; 2002 - 2005).

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M2 I2 ACIDS stands for:

Maximum, Minimum, Intercepts, Inflection points, Asymptotes,
Concavity, Increasing intervals, Decreasing intervals and Symmetry.
For notes on this topic see lesson on curve sketching.