Biocalculus: Calculus For Life Sciences
15th Edition
ISBN: 9781305177291
Author: James Stewart, Troy Day
Publisher: Cengage Learning
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Chapter 3.1, Problem 16E
To determine
To sketch: graph of a function g for which
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a) Sketch the graph of the function
f (x) = {2x – 3 if x 2
%3D
then evaluate lim f(x),
lim f(x) at a = 2.
X --> a+
X --> a-
b) Find the derivative of the following function
f (x) = 3x5 – 2x4 + 3x2 - 2x + 1
%3D
c) Find the derivative of the following function g (x) = (1+x) e
d) Find the derivative of the following function h (x) = (x + )
%3D
4. Sketch a graph of a function g(x) with g(1) = 2 and lim g(x) = 0.
x-1
2. By drawing a graph illustrate an example of a function f(x) such that it satisfies
these three conditions: lim,→1- = 2, lim,→1+ = -1 and f(1) = 0.
Chapter 3 Solutions
Biocalculus: Calculus For Life Sciences
Ch. 3.1 - Prob. 1ECh. 3.1 - Prob. 2ECh. 3.1 - Prob. 3ECh. 3.1 - Prob. 4ECh. 3.1 - Prob. 5ECh. 3.1 - Prob. 6ECh. 3.1 - Prob. 7ECh. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10E
Ch. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Prob. 13ECh. 3.1 - Prob. 14ECh. 3.1 - Prob. 15ECh. 3.1 - Prob. 16ECh. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - Prob. 20ECh. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - Prob. 31ECh. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - Prob. 39ECh. 3.1 - Prob. 40ECh. 3.1 - Prob. 41ECh. 3.1 - Prob. 42ECh. 3.2 - Prob. 1ECh. 3.2 - Prob. 2ECh. 3.2 - Prob. 3ECh. 3.2 - Prob. 4ECh. 3.2 - Prob. 5ECh. 3.2 - Prob. 6ECh. 3.2 - Prob. 7ECh. 3.2 - Prob. 8ECh. 3.2 - Prob. 9ECh. 3.2 - Prob. 10ECh. 3.2 - Prob. 11ECh. 3.2 - Prob. 12ECh. 3.2 - Prob. 13ECh. 3.2 - Prob. 14ECh. 3.2 - Prob. 15ECh. 3.2 - Prob. 16ECh. 3.2 - Prob. 17ECh. 3.2 - Prob. 18ECh. 3.2 - Prob. 19ECh. 3.2 - Prob. 20ECh. 3.2 - Prob. 21ECh. 3.2 - Prob. 22ECh. 3.2 - Prob. 23ECh. 3.2 - Prob. 24ECh. 3.2 - Prob. 25ECh. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - Prob. 29ECh. 3.2 - Prob. 30ECh. 3.2 - Prob. 31ECh. 3.2 - Prob. 32ECh. 3.2 - Prob. 33ECh. 3.2 - Prob. 34ECh. 3.2 - Prob. 35ECh. 3.2 - Prob. 36ECh. 3.2 - Prob. 37ECh. 3.2 - Prob. 38ECh. 3.2 - Prob. 39ECh. 3.2 - Prob. 40ECh. 3.2 - Prob. 41ECh. 3.2 - Prob. 42ECh. 3.2 - Prob. 43ECh. 3.2 - Prob. 44ECh. 3.2 - Prob. 45ECh. 3.2 - Prob. 46ECh. 3.2 - Prob. 47ECh. 3.2 - Prob. 48ECh. 3.2 - Prob. 49ECh. 3.2 - Prob. 50ECh. 3.3 - Prob. 1ECh. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - Prob. 9ECh. 3.3 - Prob. 10ECh. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - Prob. 13ECh. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.3 - Prob. 17ECh. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - Prob. 24ECh. 3.3 - Prob. 25ECh. 3.3 - 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- Draw a graph of a function y = f(x) compatible with the informations given below. lim f(x) = -4 lim f(x) = 7 lim f(x) = 2 I-7- lim f(x) = -2 2-7+ lim f(x) = -6 エ→-3- エ→ー lim f(r) = 3 2+-3+ lim f(x) = -00 lim f(x) = 00 lim f(x) = -00 lim f(x) = 3 lim f(x) = -2 エ→5- lim f(x) = -2 エ→5+ lim f (x) = 10 lim f(x) = 20 lim f(r) = 0 I+15 エ→8 I+11 f(-9) = 0 f(2) = 0 f(5) = -3 f(6) = 0 f(15) = -5arrow_forwardDraw a simple graph of a function f satisfying the followings: limx→2−f(x)=∞ ; limx→2+f(x)=−∞ limx→−1+f(x)=−4 ; limx→−1−f(x)=3 limx→0+f(x)=−∞ ; limx→0−f(x)=2 limx→6f(x)=0 ; limx→−4f(x)=0 limx→∞f(x)=12 ; limx→−∞f(x)=∞ ( Please do not try to formulate the function, just draw a simple graph which satisfy all above properties. )arrow_forwardSketch the graph of a function y = f(x) with all of the following properties: a) f ′(x) > 0 for −2 ≤ x < 1 b) f ′(2) = 0 c) f ′(x) > 0 for x > 2 d) f(2) = 2 and f(0) = 1 e) lim x → −∞ f(x) = 0 and lim x → ∞ f(x) = ∞ f) f ′(1) does not existsarrow_forward
- 2. For the function g whose graph is shown, state the following. (a) lim g(x) = (b) lim g(x) = x--6 (c) lim g(x)= x→0+ (e) The equations of the vertical asymptotes. -0-x (d) limg(x) = x →4 NJ Xarrow_forwardSketch the graph of a function, f(x), that has each of the following properties: • Domain: x € [-2, 1) U (1,7) U (7,00) • Range: y € (-00, 10] lim f(x) = -3 X-00 lim f(x) = -co and lim f(x) = 0 . lim f(x) = 5 X→-2+ lim f(x) does not exist X-9 The maximum output of f(x) occurs when x = 3 -10- 9 8 7 6 5 4 3 2 -1- -10-9-8-7 -6 -5 -4 -3 -2 -1 0 -1 -2 -3 -4 --5- --6- -7- -8 -9- -10- 2 3 4 5 6 7 8 9 10arrow_forward(5) Sketch the graph of a function y = f (x) that satisfies all of the following conditions. lim f(x) = -0 lim f(x) = 1 lim f(x) = = 00 I-3+ lim f(x) = –1 f (0) is undefined f(2) = –3 -4 -2-arrow_forward
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