Concept explainers
In Exercises 79-82, find a function that satisfies the given conditions and sketch its graph. (The answers here are not unique. Any function that satisfies the conditions is acceptable. Feel free to use formulas defined in pieces if that will help.)
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University Calculus
- The graph of a function f is given. A. At what numbers a does the lim x>a not exist? B. At what numbers a is f not continuous? C. At what numbers a does lim x > a exist, but f is not continuous at a?arrow_forwardSketch the graph of an example of a function f that satisfies all of the given conditions. lim x→0 (f(x)) = ∞, lim x→3− (f(x)) = −∞, lim x→3+ (f(x)) = ∞, lim x→−∞ (f(x)) = 3, lim x→∞ (f(x)) = −2arrow_forwardSketch an example of a graph of function f that meets the following conditions: Lim x > -3- f(x) = 3 Lim x > -3+ f(x) = 2 Lim x > -3 f(x) = -1 Lim x > 3+ f(x) = 2 F(-3) = 2 F(3) = 0arrow_forward
- In Exercises 1-4, use the graph of the function to find the domain D and range R of f(x) and the indicated function valuesarrow_forwardThe greatest integer function, also known as the floor function, isdefined by [ x ] = n, where n is the unique integer such that n < x < n + 1.Sketch the graph of y = [ x ] . Calculate for c an integer:(a) lim [ x ] (b) lim [ x ] ( c) lim [ x ] x→ c x→ c+ x→ 2.6arrow_forwardThe average monthly sales volume (in thousands of dollars) for a firm depends on the number of hours x of training of its sales staff, according to the following. (Give exact answers. Do not round.) S(x) = 2 x + 20 + x 2 , 2 ≤ x ≤ 100 (a) Find lim x→2+ S(x). thousand dollars(b) Find lim x→100− S(x). thousand dollarsarrow_forward
- Sketch a graph with the following characteristics: f'(x)>0, -inf<x<-1, 1<x<3 f'(x)<0, -1<x<0, 0<x<1, x>3 f"(x)>0, 0<x<2, 4<x<inf f"(x)<0, -inf<x<0, 2<x<4 f'(-1)=f'(-1)=f'(3)=0 f"(2)=f"(4)=0 lim x approaches inf f(x)=0 lim x approaches 0^- f(x)=-infarrow_forwardFind the absolute maximum and absolute minimum of the following function on the given interval.arrow_forwardUse the graph of the function f to decide whether the value of the given quantity exists. (a) f(-2) (b) lim x→−2 f(x) (c) f(0) (d) lim x→0 f(x) (e) f(2) (f) lim x→2 f(x)(g) f(4) (h) lim x→4 f(x)arrow_forward
- Let (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.arrow_forwardSketch and label a graph of a function f(x) that has the stated properties:f(-2) = 1 and limx→-2 f(x) = 1f(0) = 3 and limx→0 f(x) = 2f(1) = 4 and limx→1 f(x) does not existarrow_forward