7. Let f,g: R → R, and c Є R. 1. Prove: if both lim f(x) and lim(f + g)(x) exist in R, then lim g(x) exists in R. х-с x c x c 2. If lim f(x) and lim(fg)(x) exist in R, is that true lim g(x) exists in R? Show your x c argument. x c х-с

Q: (b) Assume that lim,6 f(r) = 9 and that lim,6 g(r) = 3. Compute lim f(r)g(r) - f (x)f(x) + g(x)g(x)

Q: (4) Let f(x) be the function whose domain is all of R given by the rule 42 if r € Z and f(x) = 10…

Q: ) State the definition of the "limit of a function": The definition begins: GIVEN: f:(x1, a)U(a, x2)…

Q: Exercise 2. Let f: (1, 00) → R and g : (0, 1) → R be such that g(x) = f(1/x). Prove that lim f(x) =…

Q: Use the graph of f(z) below to find lim f(z) 10 y -4 -2 10 a) O-3 b) O2 c) O-4 d) O-1 e) 00 f) O…

Q: State the definition of the "limit of a function": The definition begins: VEN: f:(x1,a)U(a, x:) – R…

Q: Let f,g: RR, and c E R. 1. Prove: if both lim f(x) and lim(f + g)(x) exist, then lim g(x) exists. x…

Q: -4 Determine the limit: lim -i (и — 1)2

Q: Evaluate the limit t³ - 1 1 lim t 1 ²

Q: Use the Squeeze Theorem to show that lim x2 co X-0 cos(207TX) = 0. Illustrate by graphing the…