Suppose we have applied dimensionality reduction to a dataset of m examples {x(),x(2), ...,x(m)}, where x e R". As a result of this, we will have: O a. A lower dimensional dataset {z(1),z(2), ..., z(m)} of m examples where z) e R* for some value of k and k < n. A lower dimensional dataset {z), z(2),..., z()} of k examples where k n. O @),...,z(®} of k examples where k > n. d. A lower dimensional dataset {z(1),z

Q: ƒ(z) = (z³ + z − 4); [−1,2] x h(x) ; [0,2] x-3'

A: Mean Value Theorem:  f'(c) = (f(b)-f(a))/(b-a)

Q: 2. (a) Let A = {x = [0, 1]: x has a decimal representation not containing the digit 5.} Show that A…

A: We shall use certain results from measure theory

Q: Let f(x) = (x - 3)-2. Find all values of c in (2, 5) such that f(5) – f(2) = f'(c)(5 – 2). (Enter…

A: Introduction: The mean value property is a very important and advanced property shown by a…

Q: e) Find the mean median ed (6) X ~ Bi (np). If the mean is 102 cand o² = 0.12 Find the pr(x > 1)

A:

Q: T 59-60 Estimate the intervals of concavity to one decimal place by using a computer algebra system…

A: 59. The given function fx=x4+x3+1x2+x+1 We have to find the intervals of concavity.

Q: -1 2 -4 -5 -6 -7 -3 -2 -1 1 2 Above is the graph of f(x). List the critical numbers of f.

A: The critical numbers show points where the graph has zero slope. So, they show where the graph has a…

Q: 9. (a) Verify that the function satisfies the hypotheses of Rolle's Theorem and find all values of c…

A: We have to verify the Rolle's theorem and use the Mean value theorem.

Q: 8. What is the value of c guaranteed to exist by the Mean Value Theorem if m(x) = x4 - 3x over the…

A: The answer for the above question is as shown below.

Q: 4.

A: Check that f(x) is continuous &amp; differentiable on the interval. Find the values of c The main…

Q: %3D Let C be a set in one-dimensional space and let Q(C) = Ec f(x) ,where f(x) = (3/4)(1/4)", x = 0,…

A: Just defining the  Q(c) and then proceed as given..........................

Q: The t-table has entries for areas of 0.10, 0.05, 0.025, 0.01, and 0.005. In contrast, the ?2-table…

A: The t-table has entries for areas of 0.10, 0.05, 0.025, 0.01 and 0.005 and the χ2-table has entries…

Q: The t-table has entries for areas of 0.10, 0.05, 0.025, 0.01, and 0.005. In contrast, the ? 2 -table…

A: The t-table has entries for areas of 0.10, 0.05, 0.025, 0.01 and 0.005 and the χ2-table has entries…

Q: 1)^3 , 1 ≤ x ≤ 2, S(x) = S1(x)

A: