Exercise 1. Let A, BC R. (a) Prove that if AC B, the int(A) C int(B). (b) Prove that int(AN B) = int(A) N int(B). (c) Prove that int(A) U int(B) C int(AU B).

Q: Evaluate the integral: cos 4x cos 6x dx. A) sin 2x + sin 10x + c. 20 -sin 2x + sin 10x + c. C) sin…

A: Let's find integration of given function.

Q: fio gis integable integrable 6+ = 4 that h is integrable prove

A: Given that f and g are both integrable.  To prove that h=f+g is also integrable. Let us consider a…

Q: it X- ( a,b,c,d) A= (a,c) B= (b,d), T= (X,0,(a ,b) .lc,d}} find Int (A) Int (B)

A: Interior of a set A is defined as the union of all the open sets contained in A. so in this we see…

Q: Expless the following atnction By beth integral Computer evalucate numericoN the T function and The…

A:

Q: Let h: RR be integrable on every bounded interval and h(x + y)=h(x) +h(y) for any r, y ER Show that…

A: As per the question we have a integrable function h : R ➞ R such that : h(x+y) = h(x) + h(y)  for…

Q: What is the resulting integrable form of evx+I x+1

A: We have to find value of given Integral.

Q: 3. Consider a set of numbers B = {n E Z|1<n< 900} Answer the following questions. (a) How many…

A:

Q: L* dx 1 S Int dt

A: We will use the Newton Leibnitz formula

Q: eln (R/c) secx - sec?x)" sec(34 – x) "du?? dx to be integrable using the formula What should be the…

A:

Q: prove that f(x) = { if* >1 if x≤ 1 1 x = [0₂2] is integrable Find (mis mi) and (U(P;P), L(P₂P))

A: Given:The function is .The interval is Aim:To prove the function is integrable in .To find:  and…

Q: Prove there are no natural numbers a and b such that √a+b = √a + √b.c

A: Assume such a,b exists and prove by contradiction

Q: 26. tan ³0 sec ³0 de

A: Topic = Integration

Q: Stanx secx dx a) let ustanx b) let v= sec ² x c) Explain the difference. of the answers Evaluate by…

A: To evaluate the given integral.

Q: FIND THE A BAR, ADHERENT POINTS OF A,  CLUSTER POINT OF A, INT(A), EXT(A), FR(A), DENSE OR NOT

A:

Q: (1) リ) ints where

A: As per the bartleby guidelines for more than one question only one has to be solved  please upload…

Q: Q3: If f is Riemann integrable fuction, then prove the following 1) [f] is Riemann integrable 2) f²…

A: Use the properties and definition of Riemann integral to prove this as in next step.

Q: evaluate the integral (Use a for af inteqration) the constant tu In (t) dt

A:

Q: The value of the integral (17 tan z- 17 sec r)dr = %3D O -68 O 4 O 68 O-4

A:

Q: (2x – 3y)dx – (-6y + 4x + 1 )dy = 0

A: Given that 2x-3ydx+4x-6y+1dy=0

Q: 3) int a=2,b-3,c%3; if ((a>b) || (a=b)) { c=2+a*b;

A: Since a&lt;b so the 1st condition is satisfied. So the loop will run.

Q: - sec?x)emG/e sec³x dr e In (a le) What should be the value of A for to be integrable using the…

A:

Q: In (R, 7orm), if A = R - :n EN and then Int(A)=

A: Option (B) is the correct option.

Q: 8t/3- 10t4/3 dt 8/27 t2

A: Let I=∫82718t13-10t43t2dt

Q: prove that integer V intgers is an

A:

Q: A is subset of X   Show that X=int(A) U ext(A) u Fr(A)

A: Solution:-Let X be a topological space and A⊂X. Show that X=int(A)∪Fr(A)∪ext(A), this being a union…

Q: Jine tue om example to ouow tuat inE (AnB)= Int(A)n Int(B) %3D

A: The interior of a subset S of a topological space X is the union of all subsets of S that are open…

Q: (b) Prove that Cl(AU B) = ClA U CIB.

A: The closure of S may equivalently be defined as the union of S and its boundary, and also as the…