By first principles, the derivative is
Use the binomial theorem to expand the numerator:
where
The first term is eliminated, and the limit is
A power of in every term of the numerator cancels with
in the denominator:
Finally, each term containing approaches 0 as
, and the derivative is
Answer: The answer is in the attached figure.
Step-by-step explanation: We are given to draw a net for a rectangular prism of length 8 units, width 2 units and height 3 units.
What is a rectangular prism? It is a a solid three-dimensional object consisting of six faces, where each of the face is a rectangle. The same cross-section along a length of a rectangular prism makes it a prism. We also call it as a cuboid.
As given in the question, a rectangular prism ABCDEFGH is drawn in the attached figure, where length is 8 units, width is 2 units and height is 3 units.
Option B: 5 is the value of f(3)
Explanation:
The equation of the piecewise function is given by
We need to find the value of
The value of the function f can be determined when by identifying in which interval does the value of
lie in the piecewise function.
Thus, lies in the interval
, the function f is given by
Substituting in the function
, we get,
Thus, the value of is 5.
Therefore, Option B is the correct answer.