Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 0.3, Problem 12E
a.
To determine
To find out the given operation by hand IEEE double precision computer arithmetic using rounding to nearest for the given expression.
b.
To determine
To find out the given operation by hand IEEE double precision computer arithmetic using rounding to nearest for the given expression.
c.
To determine
To find out the given operation by hand IEEE double precision computer arithmetic using rounding to nearest for the given expression.
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Chapter 0 Solutions
Numerical Analysis
Ch. 0.1 - Rewrite the following polynomials in nested form...Ch. 0.1 - Rewrite the following polynomials in nested form...Ch. 0.1 - Evaluate P(x)=x64x4+2x2+1 at x=1/2 by considering...Ch. 0.1 - Evaluate the nested polynomial with base points...Ch. 0.1 - Evaluate the nested polynomial with base points...Ch. 0.1 - Explain how to evaluate the polynomial for a given...Ch. 0.1 - How many additions and multiplications are...Ch. 0.1 - Use the function nest to evaluate P(x)=1+x+...+x50...Ch. 0.1 - Use nest.m to evaluate P(x)=1x+x2x3+...+x98x99 at...Ch. 0.2 - Find the binary representation of the base 10...
Ch. 0.2 - Find the binary representation of the base 10...Ch. 0.2 - Convert the following base 10 numbers to binary....Ch. 0.2 - Convert the following base 10 numbers to binary....Ch. 0.2 - Find the first bits in the binary representation...Ch. 0.2 - Find the first 15 bits in the binary...Ch. 0.2 - Convert the following binary numbers to base :...Ch. 0.2 - Convert the following binary numbers to base...Ch. 0.3 - Convert the following base 10 numbers to binary...Ch. 0.3 - Convert the following base 10 numbers to binary...Ch. 0.3 - For which positive integers k can the number 5+2k...Ch. 0.3 - Find the largest integer k for which in double...Ch. 0.3 - Do the following sums by hand in IEEE double...Ch. 0.3 - Do the following sums by hand in IEEE double...Ch. 0.3 - Prob. 7ECh. 0.3 - Is 1/3+2/3 exactly equal to I in double precision...Ch. 0.3 - Prob. 9ECh. 0.3 - Prob. 10ECh. 0.3 - Does the associative law hold for IEEE computer...Ch. 0.3 - Prob. 12ECh. 0.3 - Prob. 13ECh. 0.3 - Prob. 14ECh. 0.3 - Do the following operations by hand in IEEE double...Ch. 0.3 - Prob. 16ECh. 0.4 - Identify for which values of x there is...Ch. 0.4 - Find the roots of the equation x2+3x814=0 with...Ch. 0.4 - Explain how to most accurately compute the two...Ch. 0.4 - Evaluate the quantity xx2+17x2 where x=910 ,...Ch. 0.4 - Evaluate the quantity 16x4x24x2 where x=812 ,...Ch. 0.4 - Prove formula (0.14).Ch. 0.4 - Calculate the expressions that follow in double...Ch. 0.4 - Prob. 2CPCh. 0.4 - Prob. 3CPCh. 0.4 - Prob. 4CPCh. 0.4 - Prob. 5CPCh. 0.5 - Prob. 1ECh. 0.5 - Find c satisfying the Mean Value Theorem for f(x)...Ch. 0.5 - Find c satisfying the Mean Value Theorem for...Ch. 0.5 - Find the Taylor polynomial of degree 2 about the...Ch. 0.5 - Find the Taylor polynomial of degree 5 about the...Ch. 0.5 - a. Find the Taylor polynomial of degree 4 for ...Ch. 0.5 - Carry out Exercise 6 (a)-(d) for f(x)=lnx .Ch. 0.5 - (a) Find the degree 5 Taylor polynomial centered...Ch. 0.5 - Prob. 9E
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- (b) Find the (instantaneous) rate of change of y at x = 5. In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the following limit. lim h→0 - f(x + h) − f(x) h The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule defining f. f(x + h) = (x + h)² - 5(x+ h) = 2xh+h2_ x² + 2xh + h² 5✔ - 5 )x - 5h Step 4 - The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x). - f(x + h) f(x) = = (x² x² + 2xh + h² - ])- = 2x + h² - 5h ])x-5h) - (x² - 5x) = ]) (2x + h - 5) Macbook Proarrow_forwardEvaluate the integral using integration by parts. Sx² cos (9x) dxarrow_forwardLet f be defined as follows. y = f(x) = x² - 5x (a) Find the average rate of change of y with respect to x in the following intervals. from x = 4 to x = 5 from x = 4 to x = 4.5 from x = 4 to x = 4.1 (b) Find the (instantaneous) rate of change of y at x = 4. Need Help? Read It Master Itarrow_forward
- Determine whether the inverse of f(x)=x^4+2 is a function. Then, find the inverse.arrow_forwardVelocity of a Ball Thrown into the Air The position function of an object moving along a straight line is given by s = f(t). The average velocity of the object over the time interval [a, b] is the average rate of change of f over [a, b]; its (instantaneous) velocity at t = a is the rate of change of f at a. A ball is thrown straight up with an initial velocity of 128 ft/sec, so that its height (in feet) after t sec is given by s = f(t) = 128t - 16t². (a) What is the average velocity of the ball over the following time intervals? [3,4] [3, 3.5] [3, 3.1] ft/sec ft/sec ft/sec (b) What is the instantaneous velocity at time t = 3? ft/sec (c) What is the instantaneous velocity at time t = 7? ft/sec Is the ball rising or falling at this time? O rising falling (d) When will the ball hit the ground? t = sec Need Help? Read It Watch Itarrow_forwardpractice problem please help!arrow_forward
- practice problem please help!arrow_forwardFind the slope of the tangent line to the graph of the function at the given point. m = 8 f(x) = 7x at (1,3) Determine an equation of the tangent line. y = Need Help? Read It Watch Itarrow_forwardFind the slope of the tangent line to the graph of the function at the given point. f(x) = -4x + 5 at (-1, 9) m Determine an equation of the tangent line. y = Need Help? Read It Watch It SUBMIT ANSWERarrow_forward
- Find the slope of the tangent line to the graph of the function at the given point. f(x) = 5x-4x² at (-1, -9) m Determine an equation of the tangent line. y = Need Help? Read It Master It SUBMIT ANSWERarrow_forwardy = log 5 – x2 - 4 00arrow_forwardFor what value of A and B the function f(x) will be continuous everywhere for the given definition?..arrow_forward
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