New Semester Started Get 50% OFF Study Help! --h --m --s Claim Now

Question Answers

Textbooks

Find textbooks, questions and answers

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Study Help
Tutors
AI Study Planner NEW
Sell Books

Search
Sign In
Register

study help
business
statistics econometrics

Biocalculus Calculus Probability And Statistics For The Life Sciences 1st Edition James Stewart, Troy Day - Solutions

If lim x l 0 f sxd x2 − 5, find the following limits.(a) lim xl0 f sxd (b) lim x l 0 f sxd x
If lim x l 1 f sxd 2 8 x 2 1− 10, find lim x l 1 f sxd.
Prove that cosine has the Direct Substitution Property.
To prove that sine has the Direct Substitution Property we need to show that limxla sin x − sin a for every real numbera. If we let h − x 2a, then x − a 1 h and x l a &? h l 0. So an equivalent statement is that lim hl0 sinsa 1 hd − sin a Use (5) to show that this is true.
In the theory of relativity, the Lorentz contraction formula L − L0s1 2 v2yc2 expresses the length L of an object as a function of its velocity v with respect to an observer, where L0 is the length of the object at rest and c is the speed of light. Find limv l c2L and interpret the result. Why is
(a) If p is a polynomial, show that lim xl a psxd − psad.(b) If r is a rational function, use part (a) to show that limx l a rsxd − rsad for every number a in the domain of r.
lim xl0 x cot x Find the limit.
lim l 0 sin 1 tan Find the limit.
lim tl0 sin2 3t t 2 Find the limit.
lim t l 0 tan 6t sin 2t Find the limit.
lim x l 0 sin 4x sin 6x Find the limit.
lim x l 0 sin 3x xFind the limit.
Let f sxd − Hx2 1 1 sx 2 2d2 if x , 1 if x > 1(a) Find limxl12 f sxd and limxl11 f sxd.(b) Does limxl1 f sxd exist?(c) Sketch the graph of f .
Let tsxd −x2 1 x 2 6|x 2 2 | .(a) Find(i) lim x l 21 tsxd (ii) lim x l 22 tsxd(b) Does limx l 2 tsxd exist?(c) Sketch the graph of t.
lim x l 22 2 2 |x |2 1 x Find the limit, if it exists. If the limit does not exist, explain why.
lim x l 02 S1 x2 1|x |D Find the limit, if it exists. If the limit does not exist, explain why.
lim x l 26 2x 1 12|x 1 6 |Find the limit, if it exists. If the limit does not exist, explain why.
lim x l 3 s2x 1 |x 2 3 |d Find the limit, if it exists. If the limit does not exist, explain why.
Gene regulation Genes produce molecules called mRNA that go on to produce proteins. High concentrations of protein inhibit the production of mRNA, leading to stable gene regulation. This process has been modeled (see Section 10.3) to show that the concentration of mRNA over time is given by the
Prove that lim x l 0 x4 cos 2x− 0.
If 2x < tsxd < x4 2 x2 1 2 for all x, evaluate lim x l 1 tsxd.
If 4x 2 9 < f sxd < x2 2 4x 1 7 for x > 0, find lim x l 4 f sxd.
Use the Squeeze Theorem to show that lim x l 0 sx3 1 x2 sinx− 0 Illustrate by graphing the functionsf, t, and h (in the notation of the Squeeze Theorem) on the same screen.
Use the Squeeze Theorem to show that limx l 0 sx2 cos 20xd − 0. Illustrate by graphing the functions f sxd − 2x2, tsxd − x2 cos 20x, and hsxd − x2 on the same screen.
(a) Use a graph of f sxd − s3 1 x 2 s3 xto estimate the value of limx l 0 f sxd to two decimal places.(b) Use a table of values of f sxd to estimate the limit to four decimal places.(c) Use the Limit Laws to find the exact value of the limit.
(a) Estimate the value of lim x l 0 xs1 1 3x 2 1 by graphing the function f sxd − xyss1 1 3x 2 1d.(b) Make a table of values of f sxd for x close to 0 and guess the value of the limit.(c) Use the Limit Laws to prove that your guess is correct.
Evaluate the limit, if it exists. lim -4 2 x+95 x + 4
Evaluate the limit, if it exists. lim 1 1-0 1+1 t
Evaluate the limit, if it exists. lim 10 t 1
Evaluate the limit, if it exists.lim x l 16 4 2 sx 16x 2 x2
Evaluate the limit, if it exists.lim x l 21 x2 1 2x 1 1 x4 2 1
Evaluate the limit, if it exists.lim x l 24 1 4 1 1 x 4 1 x
Evaluate the limit, if it exists.lim hl0 s1 1 h 2 1 h
Evaluate the limit, if it exists.lim x l 22 x 1 2 x3 1 8
Evaluate the limit, if it exists.lim h l 0 s2 1 hd3 2 8 h
Evaluate the limit, if it exists.lim hl0 s4 1 hd2 2 16 h
Evaluate the limit, if it exists.lim x l 21 x2 2 4x x2 2 3x 2 4
Evaluate the limit, if it exists.lim t l 23 t 2 2 9 2t 2 1 7t 1 3
Evaluate the limit, if it exists.lim x l 21 2x2 1 3x 1 1 x2 2 2x 2 3
Evaluate the limit, if it exists.lim x l 5 x2 2 5x 1 6 x 2 5
Evaluate the limit, if it exists. lim x l 4 x2 2 4x x2 2 3x 2 4
Evaluate the limit, if it exists. lim x l 5 x2 2 6x 1 5 x 2 5
(a) What is wrong with the following equation?(b) In view of part (a), explain why the equation x+x-6 =x+3 x-2
Evaluate the limit and justify each step by indicating the appropriate Limit Law(s).lim ly2 sin
Evaluate the limit and justify each step by indicating the appropriate Limit Law(s).lim xl0 cos4x 5 1 2x3
Evaluate the limit and justify each step by indicating the appropriate Limit Law(s). lim 2x+1 x-2 V3x-2
Evaluate the limit and justify each step by indicating the appropriate Limit Law(s).lim tl21 st 2 1 1d3st 1 3d5
Evaluate the limit and justify each step by indicating the appropriate Limit Law(s).lim xl22 s3x4 1 2x2 2 x 1 1d
The graphs of f and t are given. Use them to evaluate each limit, if it exists. If the limit does not exist, explain why.(a) lim x l 2 f f sxd 1 tsxdg (b) lim x l 1 f f sxd 1 tsxdg(c) lim x l 0 f f sxd tsxdg (d) lim x l 21 f sxd tsxd(e) lim x l 2 fx3 f sxdg (f) lim x l 1 s3 1 f sxd y= f(x) 1 20 R
Given that lim xl2 f sxd − 4 lim xl2 tsxd − 22 lim xl2 hsxd − 0 find the limits that exist. If the limit does not exist, explain why.(a) lim x l 2 f f sxd 1 5tsxdg (b) lim x l 2 f tsxdg3(c) lim x l 2 sf sxd (d) lim x l 2 3f sxd tsxd(e) lim x l 2 tsxd hsxd(f) lim x l 2 tsxdhsxd f sxd
In the theory of relativity, the mass of a particle with velocity v iswhere m0 is the mass of the particle at rest and c is the speed of light. What happens as v l c2? m mo - v/c
Graph the function f sxd − sinsyxd of Example 5 in the viewing rectangle f21, 1g by f21, 1g. Then zoom in toward the origin several times. Comment on the behavior of this function.
(a) Evaluate the function f sxd − x2 2 s2xy1000d for x − 1, 0.8, 0.6, 0.4, 0.2, 0.1, and 0.05, and guess the value of(b) Evaluate f sxd for x − 0.04, 0.02, 0.01, 0.005, 0.003, and 0.001. Guess again. 2x lim x x-0 1000
(a) Estimate the value of the limit limxl0 s1 1 xd1yx to five decimal places. Does this number look familiar?; (b) Illustrate part (a) by graphing the function y − s1 1 xd1yx.
(a) Graph the function f sxd − ex 1 ln| x 2 4 | for 0 < x < 5. Do you think the graph is an accurate representation of f ?(b) How would you get a graph that represents f better?
Determine lim xl12 1x3 2 1 and lim xl11 1x3 2 1(a) by evaluating f sxd − 1ysx3 2 1d for values of x that approach 1 from the left and from the right,(b) by reasoning as in Example 11, and; (c) from a graph of f.
(a) Find the vertical asymptotes of the function y −x2 1 1 3x 2 2x2; (b) Confirm your answer to part (a) by graphing the function.
(a) Estimate the value of lim xl0 sin x sin x by graphing the function f sxd − ssin xdyssin xd. State your answer correct to two decimal places.(b) Check your answer in part (a) by evaluating f sxd for values of x that approach 0.29. Determine the infinite limit.lim xl231 x 1 2 x 1 3 30.
(a) By graphing the function f sxd − scos 2x 2 cos xdyx2 and zooming in toward the point where the graph crosses the y-axis, estimate the value of limxl0 f sxd.(b) Check your answer in part (a) by evaluating f sxd for values of x that approach 0.
Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places).lim hl0 s2 1 hd5 2 32 h , h − 60.5, 60.1, 60.01, 60.001, 60.0001 23. Use a table of values to estimate the value of the limit.If you have a graphing device, use it to
Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places).lim tl0 e5t 2 1 t , t − 60.5, 60.1, 60.01, 60.001, 60.0001
Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places).lim xl21 x2 2 2x x2 2 x 2 2 , x − 0, 20.5, 20.9, 20.95, 20.99, 20.999, 22, 21.5, 21.1, 21.01, 21.001
Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places).lim xl2 x2 2 2x x2 2 x 2 x , x − 2.5, 2.1, 2.05, 2.01, 2.005, 2.001, 1.9, 1.95, 1.99, 1.995, 1.999
Sketch the graph of an example of a function f that satisfies all of the given conditions.lim xl`f sxd − 2`, lim xl`f sxd − 2, f s0d − 0, f is even
Sketch the graph of an example of a function f that satisfies all of the given conditions.f s0d − 3, lim xl02 f sxd − 4, lim xl01 f sxd − 2, lim xl2`f sxd − 2`, lim xl42 f sxd − 2`, lim xl41 f sxd − `, lim xl`f sxd − 3
Sketch the graph of an example of a function f that satisfies all of the given conditions.lim xl`f sxd − 3, lim xl22 f sxd − `, lim xl21 f sxd − 2`, f is odd
Sketch the graph of an example of a function f that satisfies all of the given conditions.lim xl2 f sxd − 2` lim xl`f sxd − `, lim xl2`f sxd − 0, lim xl01 f sxd − `, lim xl02 f sxd − 2`
Sketch the graph of an example of a function f that satisfies all of the given conditions.lim xl2 f sxd − `, lim xl221 f sxd − `, lim xl222 f sxd − 2`, lim xl2`f sxd − 0, lim xl`f sxd − 0, f s0d − 0
Sketch the graph of an example of a function f that satisfies all of the given conditions.lim xl0 f sxd − 2`, lim xl2`f sxd − 5, lim xl`f sxd − 25
Sketch the graph of an example of a function f that satisfies all of the given conditions.lim xl02 f sxd − 2, lim xl01 f sxd − 0, lim xl42 f sxd − 3, lim xl41 f sxd − 0, f s0d − 2, f s4d − 1
Sketch the graph of an example of a function f that satisfies all of the given conditions. lim xl31 f sxd − 4, lim xl32 f sxd − 2, lim xl22 f sxd − 2, f s3d − 3, f s22d − 1
Drug injections A patient receives a 150-mg injection of a drug every 4 hours. The graph shows the amount f std of the drug in the bloodstream after t hours. Find lim xl122 f std and lim xl121 f std and explain the significance of these one-sided limits. f(t) (mg) 300 150 0 4 8 + 12 16 t (hours)
For the function t whose graph is given, state the following.(a) lim xl0 tsxd (b) lim xl22 tsxd(c) lim xl21 tsxd (d) lim xl`tsxd(e) lim xl2`tsxd(f) The equations of the asymptotes X
For the function R whose graph is shown, state the following.(a) lim xl2 Rsxd (b) lim xl5 Rsxd(c) lim xl232 Rsxd (d) lim xl231 Rsxd(e) The equations of the vertical asymptotes. y -3 0 2 5 R
The population of a village is Pstd, t days after June 1.Use the graph of P to state the value of each limit, if it exists. If it doesn’t exist, explain why.(a) lim tl22 Pstd (b) lim tl21 Pstd (c) lim tl2 Pstd(d) lim tl42 Pstd (e) lim tl41 Pstd (f) lim tl4 Pstd(g) lim xl5 Pstd(h) What do you
For the function h whose graph is given, state the value of each quantity, if it exists. If it does not exist, explain why.(a) lim xl232 hsxd (b) lim xl231 hsxd (c) lim xl23 hsxd(d) hs23d (e) lim xl02 hsxd (f) lim xl01 hsxd(g) lim x l 0 hsxd (h) hs0d (i) lim x l 2 hsxd( j) hs2d (k) lim xl51 hsxd
For the function f whose graph is given, state the value of each quantity, if it exists. If it does not exist, explain why. (a) lim f(x) (b) lim f(x) 1 (c) lim f(x) x-3- x-3+ (d) lim f(x) (e) f(3) x-3 4 2. 0 2- 4 X
Use the given graph of f to state the value of each quantity, if it exists. If it does not exist, explain why.(a) lim xl22 f sxd (b) lim xl21 f sxd (c) lim xl2 f sxd(d) f s2d (e) lim x l 4 f sxd (f) f s4d 4 2. 0 2 4 20
Explain the meaning of each of the following.(a) lim xl23 f sxd − ` (b) lim xl41 f sxd − 2`
Explain what it means to say that lim xl12 f sxd − 3 and lim xl11 f sxd − 7 In this situation is it possible that limx l 1 f sxd exists?Explain.
Explain in your own words what is meant by the equation lim xl2 f sxd − 5 Is it possible for this statement to be true and yet f s2d − 3?Explain.
The velocity vstd of a falling raindrop at time t is modeled by the equation vstd − v*s1 2 e2ttyv*d where t is the acceleration due to gravity and v* is the terminal velocity of the raindrop.(a) Find limt l ` vstd.(b) For a large raindrop in moderate rainfall, a typical terminal velocity is 7.5
Let f sxd − xysx 1 1d. What is limxl` f sxd? How large does x have to be so that f sxd . 0.99?
Since limxl` e2x − 0, we should be able to make e2x as small as we like by choosing x large enough. How large do we have to take x so that e2x , 0.0001?
(a) A tank contains 5000 L of pure water. Brine that contains 30 g of salt per liter of water is pumped into the tank at a rate of 25 Lymin. Show that the concentration of salt after t minutes (in grams per liter) is Cstd −30t 200 1 t(b) What happens to the concentration as tl`?
The Pacific halibut fishery has been modeled by the equation Bstd −8 3 107 1 1 3e20.71t where Bstd is the biomass (the total mass of the members of the population) in kilograms at time t. What is limtl` Bstd? What is the significance of this limit?
The von Bertalanffy growth function Lstd − L` 2 sL` 2 L0de2kt where k is a positive constant, models the length L of a fish as a function of t, the age of the fish. This model assumes that the fish has a well-defined length L0 at birth (t − 0).(a) Calculate limtl` Lstd. How do you interpret the
Virulence and pathogen transmission The number of new infections produced by an individual infected with a pathogen such as influenza depends on the mortality rate that the pathogen causes. This pathogen-induced mortality rate is referred to as the pathogen’s virulence. [The photo shows victims
The Michaelis-Menten equation models the rate v of an enzymatic reaction as a function of the concentration [S] of a substrate S. In the case of the enzyme chymotrypsin the equation is(a) What is the horizontal asymptote of the graph of v?What is its significance?; (b) Use a graphing calculator or
For the Monod growth function RsNd − SNysc 1 Nd, what is the significance of the constant c? [Hint: What is Rscd?]
Find the limit. lim [In(x2) In(x + 1)] 81%
Find the limit. lim x 1- ex 1 + 2e*
Find the limit. lim e 3x -e-3x 3x -3x
Find the limit. lim e-1/ 100
Find the limit. lim 1+x6 4 1 + xxx
Find the limit. lim (x + x) x--x
Find the limit. lim (e+2 cos 3x)
Find the limit. x-3x + x lim xxx+2
Find the limit. lim x + 1
Find the limit. lim 6 3 + 2x 3+e

Showing 1700 - 1800 of 7357

First
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Last

Step by Step Answers

Services

Sitemap
Fun
Definitions
Become Tutor
Used Textbooks
Study Help Categories
Recent Questions
Expert Questions
Campus Wear
Sell Your Books

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship
Online Quiz
Give Feedback, Get Rewards

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Student Discount
Campus Ambassador

Secure Payment

Download Our App

© 2026 SolutionInn. All Rights Reserved