Exercise 2. Let X be a topological space. Endow Xx X with the product topology. Consider the map f: X→ Xx X,x+ (x,x). Its image f(X) is the diagonal Ax = {(x,x) | x = X}.} a) Show that f is continuous.

Q: a) How many students are taking Art?

A: the number of students taking Art if given by 6+10=16

Q: 3y² - 2y-1 (-)-5y²- 2y +6

A:

Q: Evaluate x²+3x+5

A:

Q: a3-16a

A: a³−16a ⇒a(a²−16) ⇒a(a² −4²) ⇒a(a+4)(a−4)

Q: 7 11

A:

Q: 1b+1b

A: Applying  addition operation since terms with same variable  binomial addition

Q: 7,20

A:

Q: 9 b and c

A: b) We check if the denominator is 0 for any value of x.  2x2+5=0 2x2=-5 x2=-5/2 (not possible) So…

Q: 4(5+6)=

A: Given: 4(5+6)=

Q: 3. Identify all the cycles at each node of the directed graph above.

A: Cycle is defined as a path that start and end at the same vertex.

Q: A) Suppose F(xy)- М(х,у) і + N(x,y) j is a vector field on the xy plane such that F•dr = 0 Se I F•dr…

A:

Q: d. 1 3a+18 = 1 - 8 a+6

A:

Q: 36-9z

A: Given that:36-9z

Q: limx→- f(x) limo+ f(x) limx→ = = =

A:

Q: 8 13

A:

Q: 4a5b• V18a3b6

A: We have to find

Q: limx→2 f(x) = lim, ¹x→−1+ f(x) =

A: Given graph of the function fx is   1. Find :  limx→2 fx. 2. Find :limx→-1+ fx.

Q: 3(m – 5) + m

A: 3(m-5)+m=0 3m-15+m=0 add both side 15 we get 2m=15

Q: k 24

A: First we solve the inequality. ANd for that , we divide both sides by -6 .And on dividing by…

Q: dt t²Vt² – 16

A: