EXAM #2 MATH 220 CALCULUS 1- SANTILLI
SHOW ALL WORK! Calculators allowed GOOD LUCK
Differentiate the following functions (i.e. find dy/dx) or solve the limits using L’Hospital’s
Rule if necessary:
1.)
y et an x
44ln x4xx
2.)
xtany= sinh 11x2elog5 x y4sin yln(1 x)
3.)
Find y" implicitly for x y1
Simplify your answer
4.)
lim
x11
ex
x
5.)
lim
x0
ex(1 x)
x2
6.) Evaluate to 3 decimal places. Show all work.
a.)
cosh(1.5)
b.)
tanh( 0.61)
c.)
sinh 1(4)
d.)
cosh 1(1.7)
e.)
cosh(cosh( 2))
7.) A particle’s position is depicted by
S(t)t3
3
7t2
212t6
meters, where t is in sec. Find:
a.) The intervals of time where particle is slowing down and speeding up,
b.) The total distance traveled by the particle in the first 6 seconds of travel.
8.) A window has a shape of a square surmounted by a semicircle. The base of the window is
measured as having a width of 60 cm with a possible error in measurement of 0.1 cm. Use
differentials to estimate the maximum error possible in computing the area of the window.
9.) For the engine shown in figure A, a 7-inch connecting rod in an engine is fastened to a
crank of radius 3 inches. The crankshaft rotates counterclockwise at a constant rate of 200
revolutions per minute. Find the velocity of the piston when ø=π/3.
ø
37
x
Figure A
10.) Use Newton’s Method to approximate the critical number to the curve
y x3x
in the
interval [0,1] to within 3 decimal places.
11.) A sector with central angle ø is cut from a circle of radius 12 inches, and the resulting
edges are brought together to form a cone. Find the magnitude of ø so that the volume of the
cone is at a maximum.
12.) Analyze the graph of
f(x)x26x
x211x30
. State the following:
a.) Domain
e.) Crossovers
b.) Holes
f.) f’(x) analysis- CP
c.) All asymptotes (VA,HA,SA)
g.) f”(x) analysis- PI
d.) x and y intercepts
h.) Sketch the curve.
