Concept explainers
(a) Prove that
and
if these limit exist.
(b) Use part (a) and Exercise 65 to find
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Calculus: Early Transcendentals
- 1. (a) Evaluate the limit or state that it does not exist: i. lim 32-1 37-1 ii. lim V1+r-VI-x (b) Compute the derivative of f(x) x+1 at a = 2 using the limit definition of the derivative.arrow_forward2. Find a formula for f that satisfies the following conditions: lim00 f(x) lim-3- f(x) = 0, 0, lim-of(x) = 0, lim3+ f(x) = -0, lim+0f (x) = -00, f(2) = 0arrow_forwardConsider the function f(x)= Evaluate lim f(x) and lim f(x). x → 2- X+2+ O O lim f(x) = 13 x → 2" lim f(x)=11 v→ 2+ lim f(x) = 3 x → 2- lim f(x) = 13 v→ 2+ lim f(x) = 13 X→ 2- lim f(x)=3 2+ 9x-5 -x²+7 lim f(x) = 4 X→ 2" if x 2arrow_forward
- Use the Quotient Law to prove that if lim f (x) exists and is nonzero then lim x→c 1/f(x)= 1/limf(x)arrow_forward>= {x₁ 1) Consider the piecewise function g(x) = (x-2)(x-1), 3-x, a) lim g(x) x→0+ 1, Use the definition for g to evaluate the following. Show work where appropriate. c) g(0) if x ≤ 0 if 0 2 b) lim g(x) x-0-arrow_forward1. Let the function f: DCR R be defined by f(x) = lim no0 2+ ar" (a) Evaluate lim,+-1- f(x) and lim,-1+ f(x). (b) Evaluate lim,1-f(x) and lim,1+ f(r). (c) Locate and classify all the points of discontinuity, then graph the function.arrow_forward
- 3. Find lim f (x) where if r+3 f (x) = if r= 3arrow_forward3) Suppose that the limit of f(x) exists at z = 1 and let lim f(x) = 5. Find the following limits (a) lim f(r) (b) lim f(r)arrow_forwardUse the given graph of f to state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.) (a) lim f(x) x → 2- 3 (b) lim f(x) x → ·2+ 1 (c) lim_f(x) X→ 2 DNE (d) f(2) 3 (e) lim f(x) X→ 4 4 (f) f(4) 4 X y 4 -2 0 2 4 xarrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,