B. Given any two positive numbers x and y, we define their geometric, harmonic, and arithmetic means respectively by: 2 X √xy, 1 1 2 + x y + 1) Which of these 3 numbers is the smallest? The biggest? How can we demonstrate it? 2) What is the limit of each of these 3 numbers when x or y tends to +∞o?

Q: 3.Determine the intersection X ∩ Y. Express the  in interval notation. X = {x/ x>equal 8} and Y =…

A: We have: X=x  x≥8=[8,∞)Y=x  x<7=(-∞,7)

Q: 50 50 51 7. + 40 39 40 • () - €) (") - () () - () () 7 8. 4 10 9. 2 10 8 8. 8 8. 10. + 2 3 6.

A: We can solve the given problem using concept of fractions.

Q: 4x 4 lim,-1* - x-1 In x 4 3 5 1 O 2

A:

Q: 21.) lim √9th -3 h+o h

A: The given limit limn→09+n-3n

Q: lim x→1    x² + x -2/x - 1

A: To solve the problem we have to insert the value in the given function

Q: 7x99 + 2 lim 1. Determine the limit of the following: e3x а. 7 b. 1 С. d. 0

A: L hospital rule

Q: 7. lim /* √x² + 8 dz h→0

A:

Q: 1. Evaluate each of the following limits: sin q-sin a c. lim q-a

A: We apply L- hospital rules.

Q: Find the following limits : 1+2 +3+...+x 4) lim X00 x2

A: Ans:  We have to Evaluate  the limit              limx→∞ 1+2+3+‐‐‐+xx2

Q: _6. lim x-2 \x-1 A. -2 В. 2 С. О D. DNE

A: Here, we need to find the given limit. So,          limx→ 2xx-1Plug in the value x=2=22-1=2

Q: for any natural number m. evaluate I/m +3x" + 6)" dx, x > 0. 3m 2m +x" ) ( 2x' 2m

A: Given integral can be evaluated as shown below

Q: If x > 8 and x n+1 - - for nEN. Then the limit of x is equal to 11 X 21

A: Given that, If x1>8 and xn+1=2-1xn for n∈ℕ. The objective is to find the limit of xn.

Q: 6. a) State why the limit of f(x) = √5x - 1 does not exist for x

A: Please refer to the image below

Q: (1++*+) ... 2 22 2k

A: Given below the detailed solution

Q: Consider the following figure.  m<1=7(x+3) m<3=4x-2 m<5=5(x+2)-3 Find x, m<1, m<3, and m<5

A:

Q: Find lim (a + 2ar + 3ar² + n→∞ .. +nar"-¹) where |r|< 1.

A:

Q: Find the following limits : 1+2+3+ .+ x 4) lim x2

A:

Q: O A В D All of the Above C

A: From the given graph find out which function has a domain of all real numbers

Q: |r+7| 9. b. lim r-8- x2 + 7x -8, x + 8

A:

Q: If Xo and X, are two numbers with Xo < X, then the true one is

A: Answer:-  Option D is the correct answer.

Q: Determine the union X ∪ Y. Express them in interval notation. X = {x/x>-17 } and Y = {x/x<equal-10…

A: The union of two sets A and B is defined as the set of all the elements which lie in set A and set B…