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  ?).
.
M_{2 }I_{2 }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.