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Based on the image attached, please help me solve this calculus question with a detailed solution. Thank You in advance.
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- 1.3 Evaluate the limit limz→2+i[(z-1)(3-2i)+1-3i] and use the definition of the limit (ε - δ) to verify this limit.6. Given the function f(x)= { 3x, if x< -2 -x2-2, if -2 ≤ x < 2 x-4, if 2 ≤ x < 5 √ x, if x≥5, determine which among the following limits do not exist. (there are multiple) a. lim f(x) x→5 b. lim f(x) x→2 c. lim f(x) x→-2 d. lim f(x) x→0Find the limit lim x→∞ (1+5/x)x lim x→0 ((e2x-1-x)/x2)
- 4 Given f(x), g(x) are both continuous at x = 2, f(2) = 5, andg(2) = 3; evaluate limx→2 3f(x)/g(x)(b) If we keep the first part of the hypothesis of Theorem 5.3.6(L’Hospital’s Rule) the same but we assume that lim f'(x)/g'(x) = ∞, x→a does it necessarily follow that lim f(x)/g(x)= ∞?, x→aFind the limits a lim X→5 (x2-5x) / (x2-3x -10) b lim X→0 (1-square root (1-x2)) / x c lim X→ 3/x-1 - 3/x2-x d. lim X→infinty (4x3-7x+5) / 2x3+8)
- Let f(x) = 1-x if x≤3 and f(x) = 3x-1-x2 if x>3. Which of the following limits exist as a real number ? a) limx→3 f(x) b) limx→-∞ f(x) c) limx→∞ f(x) d) limx→3- f(x) e) None of the above.Using the ε − N definition of a limit, prove that lim(n→∞)=(6n^3 −2n+1)/(2n^3+1)=3. The expert missed the first part of the question which asks for the ε − N definition.6. Evaluate the following limitsa. limx→9 3−√9 / 9−xb. lim x→0 √1+x−√1−x / xc. lim x→−2 x+2 / x2+z−2
- Find the limit. lim x → 2− e3/(2 − x)A. i. Using Arithmetic of Limits, find limn→∞ 2n / (3n + 5) . (2n devided 3n+5..ii. Working directly from the definition of limits, give a direct verification that your answer in (i) is correct. (Your answer should involve the letter ε.)4.4 worksheet 9 from 4/9/19 evaluate limit lim as x apporaches negative infinity = 9-4x/square root of 7x2 +3