Download - Math 54 Exam 1 Review
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Reminders Coverage Sample questions
Mathematics 54First Long Examination
02 September 2014, Tuesday
Discussion class room and time
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Reminders Coverage Sample questions
Math 53 methods of integration!!!
Integration by parts:∫
udv = uv−∫
v du
Trigonometric integralsfactoring out sinu, cosu, sec2 u, csc2 u, secu tanu, cscucotuidentities
Trigonometric substitutionp
a2 −u2p
a2 +u2p
u2 −a2
Partial fractionsdistinct linear factors, repeated linear factorsdistinct quadratic factors, repeated quadratic factors
Improper integralsinfinite limit/s of integrationinfinite discontinuity at point on the interval of integration
Differential equationsgeneral/particular solution of a separable differential equationapplications (e.g. orthogonal trajectories, exponentialgrowth/decay) 2 / 9
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Reminders Coverage Sample questions
Find the antiderivative:∫
(cosx+csc2 x)2 dx
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Reminders Coverage Sample questions
Evaluate the integral∫ p
π
0x3 sinx2 dx.
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Reminders Coverage Sample questions
Find the antiderivative:∫
xpx2 −4x
dx
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Reminders Coverage Sample questions
Find the antiderivative:∫
x3 +3x−2
x2(x2 +3)dx
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Reminders Coverage Sample questions
Determine whether the improper integral is convergent or
divergent:∫ +∞
−∞e−|x| dx
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Reminders Coverage Sample questions
Find the equation of the curve for whichd2y
dx2 = 1
(2x+4)2 and that is
tangent to the x-axis at the point(− 3
2,0
).
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Reminders Coverage Sample questions
Find the orthogonal trajectories to the family of curves
y = 1px−k
, k < x.
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