Solution:
Find the equation represented by the graph shown below.
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Graph of the parabola.
Directrix:
Focus:
Vertex:
Therfore,
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Rewrite the eqn. to the standard form
Solution:
031-T2-15
031-T2-14
Eqn of the left half
or
Eqn of the right half.
Thus,
Solve for x to find the eqns of the right and left sides of the ellipse.
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Eqn of the ellipse
This is the graph of the right half of a standard ellipse.
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Choose
Solve for
We can only solve for either or in terms of the other.
Compute the dot product and set it to zero.
u and v are orthogonal
then
Let
Solution:
Find a nonzero vector that is perpendicular ot the vector u = < -2, 7>
Section 7.3
Find the vertex, focus and the directrix of the parabola .
Section 8.1
031-T2-17
031-T2-13
031-T2-12
For the vectors u, v and w shown in the figure, which one of the following relations is TRUE?
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Thus,
You may choose any real number for
To find the point of intersection:
Therefore, the intersection will be in the Quadrant I only.
The fact that y is under the square root ==> that y must be positive.
The fact that x is equal to the squre root of something ==> x must be positive.
Solution:
031-T2-16
Therefore, the equation of the ellipse is:
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or
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or
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Substitute in the second equation
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and
Foci:
Center:
Complete the squares
Solution:
031-T2-9
Section 8.2
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and
Center:
Midpoint formula
Form of the ellipse read from the given foci
Solution:
031-T2-11
031-T2-10
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Which one of the following is FALSE?
Section 6.6
031-T2-19
Section 6.5
031-T2-5
Section 6.4
or
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or
Solution:
Find the number of solutions of the equation over the interval [0, 3p /2)
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Section 6.3
031-T2-2
033-T2-1
Section 6.2
Section 6.1
A. M. Farhat
Old Exams Problems
Math002
031-T2-4
031-T2-6
031-T2-7
031-T2-22
031-T2-3
Ans. 1
Ans:
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and
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or
Rewrite the eqn
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The zeros of f(x) are obtained by setting f(x) = 0 and solving for x.
Solution:
Find the zeros of the function in the interval [0, 2p)
031-T2-22
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Recall:
Solution:
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Solve for x.
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k is an integer.
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Solution:
Find the set of solutions of the equation sin3x = 1.
Find all the solutions of the equation ,
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Expand the cosine of the difference
Apply cosine to both sides.
Rewrite the eqn.
Solve the equation for x.
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The number of solutions is 4.
or
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Note: is not a solution since is not defined.
or
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or
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Divide by sin(x) and consider that sin(x) =0 may include solutions.
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Solution: