By evaluating the piecewise function and the two side limits, the limit does not exist for the function at x = 2. (Correct choice: D)
<h3>What is the limit of a piecewise function at a given value of x?</h3>
Herein we have a piecewise function formed by three parts, two linear equations and a point. The limit of the function at a given value exists if the lateral limits and the function evaluated at that point brings out the same result.
By direct inspection, we find that the left limit of the function when x tends to 2 tends to 4, likewise with the right limit, but piecewise function is equal to 2 when we evaluate it at x = 2. Therefore, by evaluating the piecewise function and the two side limits, the limit does not exist for the function at x = 2. (Correct choice: D)
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For any arbitrary 2x2 matrices
and
, only one choice of
exists to satisfy
, which is the identity matrix.
There is no other matrix that would work unless we place some more restrictions on
. One such restriction would be to ensure that
is not singular, or its determinant is non-zero. Then this matrix has an inverse, and taking
we'd get equality.
Answer: Yes it is possible
Example: Yeast is a single-celled fungus.
There are probably other types of fungus that are single-celled. However, some other fungi are multi-celled. You will likely need more information about the organism under the microscrope before you can classify it properly.
Answer:
I'm sure 4*4 means 4x4=16