Concept explainers
Let
(a) Find
(i)
(ii)
(b) Does limx→2 g(x) exist'!
(c) Sketch the graph of g.
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EBK CALCULUS EARLY TRANSCENDENTALS
- 5X²+1 IF X<\ Let F(X) = {(x-2) IF XZ1 a, Find Limx→ 1¹ and lim x→# f(x) b. does Lim X→1 f(x) exist? C. Sketch the graph of farrow_forward1) Consider the graph of function f(x): Evaluate: (a) lim f(x) x+-2- Ay 5- (b) lim f(x) x-2+ (c) lim f(x) X-2 (d) f(-2) -> (e) Is f continuous at x =-2? Explain. -5 -2-arrow_forwardLet f(x)=2x+5. Find lim h-0 (f(a+h)-f(a)/h)arrow_forward
- 4) Let f(x) = x-31, Find (a) lim f(x) x-3+ (b) lim f(x) x-3 (c) lim f(x) X-3 X-3arrow_forwardUse the graph of f(x) below to answer the following questions: y 4 N y=f(x) 3 C) Find lim f(x) x→3 A) Does lim f(x) exist? [Select] x 4 B) Find lim f(x). [Select] x→2+ 4 D) Find f(6). [ [Select] [Select] 5arrow_forwardf(2 + h) – f(2) 2 if f(x) = x² +7. Find lim h h→0 f(2 + h) – f(2) lim (Simplify your answer.) h→0arrow_forward
- 2. A portion of the graph of the function y = f(x) is shown in the figure. (a) State the domain and range of f. (b) Find the values: f(-2) and f(3). (c) Use the graph to determine each of the limits: (i) lim f(x); lim f(x); lim f(x) x-2+ x-2- x-2 (ii) lim f(x); lim f(x); x-3 lim f(x). x+3 3. The graph of the function y = k(x) is shown in the figure. (a) Write a piecewise formula for the function k. (b) Evaluate the one-sided limits of k at x = 1 algebraically, by using your formula from part (a). y=f(x) 1+ fif 1 -1- 2 1.5 1 4. Let f(x) = |x| and g(x) = x - 3. (a) Determine the formulas for each of the related composite functions: h(x) = (fog)(x) = f(g(x)) s(x) = (gof)(x) = g(f(x)) t(x) = (gofᵒg)(x) = g(f(g(x))). 5. (a) Find the values of x₁ and x₂ in the figure. (b) Find the largest positive number 8 such that: |-1|<0.1 whenever 0<|x-1|<8. Hint: Choose to be the minimum value of |x-1| for i = 1,2. (b) Plot graphs of all the functions: f,h, s, and t in the same coordinate plane. Use…arrow_forwardc) lim f(x) x-1 2x - 1 if x 2 a) lim f(x) x→2- b) lim f(x) x→2+ c) lim f(x) X-2 3. Sketch the graph of a function that satisfies the following conditions: f(3) = 1 ; lim f(x) = -3; lim f(x) = 0: lim f(x) DNE %3D x-3- x-3+ x-3 Section 2.3: Evaluate the following limits. MacBook Air 吕0 DII O00 F3 F4 F5 F6 F7 F8 F9arrow_forwardIf f(x) = 3x2 - 4x +1 and g(x) = x² + 2x - 3, then what is lim 9X, g(x). X-1 f(x)arrow_forward
- Give an example by sketching the graph of a function f that satisfies all the given conditions. lim (x--> -3) f(x)=+oo, lim (x--> -oo) f(x)=-2, f(0) = 0, f is even.arrow_forwardConsider the function f(x) whose graph is shown below:arrow_forward2. (a) Draw the graph of f(x) 2x -1 |x-1| x 0 (b) Find lim f(x) and lim f(x) or explain why they do not exist. Give reasons for x →0 your answers.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage