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Math
Calculus
Calculus: Early Transcendentals, Enhanced Etext
Chapter 5.10, Problem 53ES
Chapter 5.10, Problem 53ES
BUY
Calculus: Early Transcendentals, Enhanced Etext
12th Edition
ISBN:
9781119777984
Author: Howard Anton; Irl C. Bivens; Stephen Davis
Publisher:
Wiley Global Education US
expand_less
1 Limits And Continuity
2 The Derivative
3 Topics In Differentiation
4 The Derivative In Graphing And Applications
5 Integration
6 Applications Of The Definite Integral In Geometry, Science, And Engineering
7 Principles Of Integral Evaluation
8 Mathematical Modeling With Differential Equations
9 Infinite Series
10 Parametric And Polar Curves; Conic Sections
11 Three-dimensional Space; Vectors
12 Vector-valued Functions
13 Partial Derivatives
14 Multiple Integrals
15 Topics In Vector Calculus
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5.1 An Overview Of The Area Problem
5.2 The Indefinite Integral
5.3 Integration By Substitution
5.4 The Definition Of Area As A Limit; Sigma Notation
5.5 The Definite Integral
5.6 The Fundamental Theorem Of Calculus
5.7 Rectilinear Motion Revisited Using Integration
5.8 Average Value Of A Function And Its Applications
5.9 Evaluating Definite Integrals By Substitution
5.10 Logarithmic And Other Functions Defined By Integrals
Chapter Questions
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Problem 1QCE: 11/e1tdt=
Problem 2QCE: Estimate In 2 using Definition 5.10.1 and (a) a left endpoint approximation with n=2 . (b) a right...
Problem 3QCE: 1/ln=
Problem 4QCE: A solution to the initial-value problem dydx=cosx3.y0=2 that is defined by an integral is y=
Problem 5QCE: ddx0ex11+t4dt=
Problem 1ES
Problem 2ES
Problem 3ES: Given that lna=2 and lnc=5 , find (a) 1ac1tdt (b) 11/c1tdt (c) 1a/c1tdt (d) 1a31tdt .
Problem 4ES: Given that lna=9 , find (a) 1a1tdt (b) 12a1tdt (c) 12/a1tdt (d) 2a1tdt .
Problem 5ES: Approximate ln5 using the midpoint approximation with n=10 , and estimate the magnitude of the error...
Problem 6ES: Approximate ln3 using the midpoint approximation with n=20 , and estimate the magnitude of the error...
Problem 7ES: Simplify the expression and state the values of x for which your simplification is valid. (a) elnx...
Problem 8ES: (a) Let fx=e2x . Find the simplest exact value of the function fln3 . (b) Let fx=ex+3ex . Find the...
Problem 9ES
Problem 10ES: Express the given quantity as a power of e . (a) x (b) x2x,x0
Problem 11ES: Find the limits by making appropriate substitutions in the limits given in Theorem 5.10.8 . (a)...
Problem 12ES
Problem 13ES: Find gx using Part 2 of the Fundamental Theorem of Calculus, and check your answer by evaluating the...
Problem 14ES: Find gx using Part 2 of the Fundamental Theorem of Calculus, and check your answer by evaluating the...
Problem 15ES
Problem 16ES: Find the derivative using Formula 18 , and check your answer by evaluating the integral and then...
Problem 17ES: Let Fx=0xsintt2+1dt . Find (a) F0 (b) F0 (c) F0 .
Problem 18ES
Problem 19ES: True-False Determine whether the equation is true or false. Explain your answer. 11/a1tdt=1a1tdt,...
Problem 20ES: True-False Determine whether the equation is true or false. Explain your answer. 1a1tdt=121a1tdt,...
Problem 21ES: True-False Determine whether the equation is true or false. Explain your answer. 1e1tdt=1
Problem 22ES: True-False Determine whether the equation is true or false. Explain your answer....
Problem 23ES: (a) Use Formula 18 to find ddx1x2t1+tdt (b) Use a CAS to evaluate the integral and differentiate the...
Problem 24ES: Show that (a) ddxxaftdt=fx (b) ddxgxaftdt=fgxgx .
Problem 25ES: Use the results in Exercise 24 to find the derivative. (a) ddxxcost3dt (b) ddxtanxt21+t2dt
Problem 26ES: Use the results in Exercise 24 to find the derivative. (a) ddxx01t2+12dt (b) ddx1/xcos3tdt
Problem 27ES: Find ddx3xx2t1t2+1dt by writing 3xx2t1t2+1dt=3x0t1t2+1dt+0x2t1t2+1dt
Problem 28ES: Use Exercise 24b and the idea in Exercise 27 to show that ddxhxgxftdt=fgxgxfhxhx
Problem 29ES: Use the result obtained in Exercise 28 to perform the following differentiations: (a) ddxx2x3sin2tdt...
Problem 30ES
Problem 31ES: Let Fx=0xftdt , where f is the function whose graph is shown in the accompanying figure. (a) Find...
Problem 32ES: Determine the inflection point(s) for the graph of F in Exercise 31 .
Problem 33ES
Problem 34ES: Express Fx in a piecewise form that does not involve an integral. Fx=0xftdt , where fx=x,0x22,x2
Problem 35ES: Use Formula 11 to solve the initial-value problem. dydx=2x2+1x,y1=2
Problem 36ES: Use Formula 11 to solve the initial-value problem. dydx=x+1x,y1=0
Problem 37ES: Use Formula 11 to solve the initial-value problem. dydx=sec2xsinx,y/4=1
Problem 38ES
Problem 39ES: Suppose that at time t=0 there are P0 individuals who have disease X , and suppose that a certain...
Problem 40ES: Suppose that t is the velocity function of a particle moving along an s-axis . Write a formula for...
Problem 41ES: The accompanying figure shown the graphs of y=fx and y=0xftdt . Determine which graph is which, and...
Problem 42ES: (a) Make a conjecture about the value of the limit limk01btk1dtb0 (b) Check your conjecture by...
Problem 43ES: Let Fx=0xftdt , where f is the function graphed in the accompanying figure. (a) Where do the...
Problem 44ES: CAS programs have commands for working with most of the important nonelementary functions. Check...
Problem 45ES: The Fresnel sine and cosine functions Sx and Cx were defined in Formulas 13 and 14 and graphed in...
Problem 46ES: Find the limit limh01hxx+hlntdt
Problem 47ES: Find a function f and a number a such that 4+axftdt=e2x
Problem 48ES: (a) Give a geometric argument to show that 1x+1xx+11tdt1x,x0 (b) Use the result in part (a) to prove...
Problem 49ES: Use a graphing utility to generate the graph of y=1+1xx+11+1xx in the window 0,1000,0.2 , and use...
Problem 50ES: Prove: If f is continuous on open interval and a is any point in that interval, then Fx=axftdt is...
Problem 51ES
Problem 52ES
Problem 53ES
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