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- The graph of f(x) = 2x2/(x2 + 2) is shown. (a) Find L = limx ∞ f(x). (b) Determine x1 and x2 in terms of ε. (c) Determine M, where M > 0, such that ∣ f(x) − L∣ < ε for x > M. (d) Determine N, where N < 0, such that ∣ f(x) − L∣ < ε for x < N.1. Evaluate lim (2x-5) given its graph below. x →2 a.0 b. -1 c. 2 d. 1 2. Given the graph of f(x) below, evaluate its limit as x approaches 3. a.2 b. 3 c. 1 d. 0f'(x) = (x-1)(x-2)(x-3)(x-4) What can be said about lim(x->infinity) if anything?
- Find the limit of lim((9+3x)1/2-3)/x as x approaches 0Find the vertical and horizontal asymptotes. For the horizontal asymptotes you need to find the lim f(x) as x aproaches negative infinity and positive infinity f(x) = x/(x2-1)Evaluate lim as x approaches negative infinity 3e^2x + 4e^-x / e^2x - 2e^-x .
- If 2x+2 ≤ f(x) ≤ x2 +2x+2, for all x, then find lim f(x) x-> 0Let (x) = |x - 2| / x - 2 A) what is the domain of g(x)? B) Use numerical methods to find lim x—> 2- g(x) and lim x—> 2+ g(x). C) based on your answer to (b), what is lim x—> 2 g(x)? D) sketch an accurate graph of g(x) on the interval [-4,4]. Be sure to include any needed open or closed circles.While using the difference quotient, how do you find f'(2) using f'(a)=lim f(a+h)-f(a) for f(x)=2x2 +5x-3 h->0 h