Prove the following property about subdifferential, affline transformation. - əf(x) = {Vf(x)} if ƒ is differentiable at r – affine transformation of variables: if g(x) = f(Ax +b), then dg(x) = ATaf(Ax + b)

Q: How many even 3-digit numbers can be formed from the digits 1, 3, 4, 8, and 9 with no repetitions…

A: Out of the total 5 digits 1, 3, 4, 8 and 9 given, the even digits are 4 and 8. For the 3- digit…

Q: 4 2 G F -8 -4 -2 2 10 -2 -4 E 10 K 00

A: Formula for area is length multiply by breadth. Similarly for square its a^2 if side of square is…

Q: How many ordered triples of letters are there taken from the letters A, T, C, and G?

A: given letters: A,T,C and Gtotal number of letters = 4

Q: Find L{1}ℒ{1}.

A:

Q: Prove that X Pn dx %3D

A: Recurrence relation.  Partial fraction.

Q: 10 8/10 + 9 7/12=

A:

Q: 4. Determine (16-912) dt c4

A: We will solve the problem.

Q: -7 5 1 9 0 -2 -1 2 -1 4

A:

Q: 4n – 1

A:

Q: (5V3)2

A: Explanation of the solution is given below...

Q: 7/2 + 3 4/6

A:

Q: 5/14+1/6

A: 514+16=15+742

Q: Prove that the number of partitions of n into at most k parts is equal to that of partitions of n +…

A: given , number of partitions of n into k parts  we have to prove that , partitions of number n + k…

Q: find  3/4 + 1/8

A:

Q: 16 2/5- 8 4/9

A:

Q: 1/4 +5/4

A: Solution: The objective is to find the value of the given expression

Q: 6 2/5 ÷ 4

A: Given query is to solve the expression.

Q: 10. Find the sum of the coefficients of (2x– 3)°. c. -6560 d. -5120 а. -5660 b. -6780

A:

Q: [ 8x³(4x² + 1)12dx

A:

Q: 5 7/12 + 1 3/4 + 4 1/2

A: Given that 5712+134+412Solution  :5712+134+412=57+39+24612

Q: There are 1/8 blue balls, 1/4 green balls, 1/12 red balls and there are 26 white balls. How many…

A:

Q: 1/5 + 1/10 + 1/15

A: Sum of numbers

Q: 57-24

A: Given that: 57-24

Q: 6 3/20 - 6 3/8

A:

Q: Compute the indicated product.   -1 3   9 2 0   3 9 3

A:

Q: 5 2/5+ n= 75/6

A: Given query is to find the value of n.

Q: 8-12 (²

A: -83

Q: 4 1/2 +6 1/5=

A: We have

Q: (5/6)3

A: Cube means multiplying three times:   563=56×56×56=5×5×56×6×6=5363=125216

Q: 土4 7

A:

Q: 22 7/8 - 7=

A: Given,

Q: nvert

A:

Q: How many different ways could you choose any 4 gumballs from the 25 gumballs in the…

A: We can choose 4 gumballs from the 25 gumballs in 25C4 ways.