Answer:
Step-by-step explanation:
The question relates with rules of indices
(a) The give expression is presented as follows;
By expanding the expression, we get;
Collecting like terms gives;
(b) The given expression is presented as follows;
Therefore, we get;
Collecting like terms gives;
The disk method will only involve a single integral. I've attached a sketch of the bounded region (in red) and one such disk made by revolving it around the y-axis.
Such a disk has radius x = 1/y and height/thickness ∆y, so that the volume of one such disk is
π (radius) (height) = π (1/y)² ∆y = π/y² ∆y
and the volume of a stack of n such disks is
where is a point sampled from the interval [1, 5].
As we refine the solid by adding increasingly more, increasingly thinner disks, so that ∆y converges to 0, the sum converges to a definite integral that gives the exact volume V,
Answer:
(a) If f and t are both even functions, product ft is even.
(b) If f and t are both odd functions, product ft is even.
(c) If f is even and t is odd, product ft is odd.
Step-by-step explanation:
Even function: A function g(x) is called an even function if
Odd function: A function g(x) is called an odd function if
(a)
Let f and t are both even functions, then
The product of both functions is
The function ft is even function.
(b)
Let f and t are both odd functions, then
The product of both functions is
The function ft is even function.
(c)
Let f is even and t odd function, then
The product of both functions is
The function ft is odd function.