CALCULUS I TEST #3

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.

A/ Differentiate :

 1) 2) f (x) = ln (cos 2x + sin 2x) – 5 arcsec x² 3) g (t) = ln² (3t + 1) 4) h (x) = csc (ln x) + arctan 5x – arccos (x³ + 7) 5) y = e x ² – 3 + (7) x – 1/ x – log 3 (x³ – 5x)

(15)

B/ Use implicit or logarithmic differentiation to find y'.

1) y ² e 2x + xy³ = 1

2) y = (x + 4) x ² – 1 .

(6)

C/ Find an equation for the tangent

1) to the curve y = e – x , perpendicular to 2x – y = 5.

2) to y = ln x at the point where x = 2.

(7)

D/

1) Rewrite as an algebraic expression in x: (diagram)
 a) sec [arctan (x + 1)/5] b) sin {arccos ( –7/x)}

(4)

2) Find equations for the tangent and normal lines to the graph of
y = arcsin (x – 1) at point
.

(4)

3) Sketch the graph and list the M2I2ACIDS features of y = e – x ² ,
Clearly indicate y' and y''.

(10)

4) Solve this differential equation for f (x) if

(4)

TOTAL (50)

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

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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.