Calculus I (Math 251A) - Test 1
(No Work - No Credit)
Problem 1. [10 Points] Find t.he equat.ion for the tangent line to the graph
of t.he function f(x) = x 2 cos:r at the point:r = 7r/3.
Problem 2. [10 Points] Differentiate f(x) = jX using first principles,
Problem 3. [10 Points] Find the following limits:
,
11m
t-.l
e +') t -
t- - 1
2
and
lim
4-x
vx
--r=:;:==7'
2
x~4 5 9
+
Problem 4. [10 Points] Show that f (x) = x 3 - 7rX + J2 has a root between
l' = 1 and x = 2. Provide a careful, complete argument.
Problem 5. [10 Points] Use approximation by differentials to find an ap­
proximate value for sec 46°.
Problem 6. [10 Points] A particle moves along the parabola y = x 2 in
the first quadrant in such a way that the x-coordinate (measured in meters)
increases at a st.eady 10 meters per second. How fast is the angle of inclination
e of the line joining t.he particle to the origin changing when x = 3 meters?
Problem 7. [10 Point.s] Find the slope of the curve x 3
folium of Descartes) at the point (4,2).
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