A. Calculate each of the following limits, or explain why it does not converge. You may use any theorems that were stated in lecture. i. limx→ 1+ |x-21 / (x-2) ii. limx→ 1+ |x-1| iii. limx-1+ |x-1|/(x-1)²

Q: Find the limit

A:

Q: (Extra credit, 10 points) Let x0 = a, x₁ = b, x2 = (x0+x1) /2 and x = (xn-1+xn-2)/2. Show that In…

A: ⏹️ Approach to solving the question: Here are steps to derive the formula for xn as given in the…

Q: Determine the following limits analytically.

A: Given limx→3x2-9x2+42x2-3x-9 By using  a2-b2=(a-b)(a+b)

Q: 1. Find the limit. Show your steps. x²-x-6 x-3x²7x + 12 (a) lim (b) lim h-0 (4 + h)² - 16 h

A:

Q: If (an) has a decreasing subsequence, then (an) does not tend to infinity.

A: False

Q: 7e+e Ar 10e Ax+2e-3er (b) Find the horizontal aysmptote(s) of h(x) : If there are none, describe the…

A:

Q: D. Calculate each of the following limits, or explain why it does i. limx-1 (x-2)/(x-1)² ii. limx-1…

A:

Q: Which of the following limits represents f (3) if f(x)= 4x². O A. [(4x? + 1) + n]-37 lim h→0 O B.…

A: we have given f(x).  We have to find f'(3)

Q: Estimate the limit numerically. x² lim x+4 O diverges to +o 00 O diverges to -∞

A: Given

Q: Find the limits. Show your steps. x²-9 x 3 x²7x+12 (a) lim (b) lim x 3 x 3 (c) lim h-0 √1+h-1 h

A: