In Exercises 1–4, use the given table of values to estimate, for the given value of a, each of the following if they exist: (a) lim x → a − f ( x ) (b) lim x → a + f ( x ) (c) lim x → a f ( x ) (d) f ( a ) if it is defined [HINT: See Example 1-3 ] a = 2 ; table of values: x 1.9 1.99 1.999 1.9999 2 2.0001 2.001 2.01 2.1 f ( x ) –5.975 –5.9975 –5.99975 –5.999975 –4 440,000 44,000 4,400 440
In Exercises 1–4, use the given table of values to estimate, for the given value of a, each of the following if they exist: (a) lim x → a − f ( x ) (b) lim x → a + f ( x ) (c) lim x → a f ( x ) (d) f ( a ) if it is defined [HINT: See Example 1-3 ] a = 2 ; table of values: x 1.9 1.99 1.999 1.9999 2 2.0001 2.001 2.01 2.1 f ( x ) –5.975 –5.9975 –5.99975 –5.999975 –4 440,000 44,000 4,400 440
Solution Summary: The author concludes that as x approaches 2 from the left, the corresponding values of f(x) are +infty .
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
Find the exact area inside r=2sin(2\theta ) and outside r=\sqrt(3)
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