CALCULUS: EARLY TRANS. (LL)W/WEBASSIGN
8th Edition
ISBN: 9780357019788
Author: Stewart
Publisher: CENGAGE L
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Chapter G, Problem 2E
Refer to Example 1.
- (a) Find the equation of the tangent line to the curve y = 1/t that is parallel to the secant line AD.
- (b) Use part (a) to show that ln 2 > 0.66.
EXAMPLE 1
- (a) By comparing areas, show that
- (b) Use the Midpoint Rule with is n = 10 to estimate the value of ln 2.
FIGURE 3
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3.9 (A/B). A beam ABCDE, with A on the left, is 7 m long and is simply supported at
Band E. The lengths of the various portions are AB 1-5m, BC = 1-5m, CD = 1 m and DE
: 3 m. There is a uniformly distributed load of 15kN/m between B and a point 2m
to the right of B and concentrated loads of 20 KN act at 4 and 0 with one of 50
KN at C. (a) Draw the S.F. diagrams and hence determine the position from A at
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the B.M. diagram approximately to scale, quoting the principal values. [3.32 m, 69.8
KNm, 0, 30, 69.1, 68.1, 0 kNm.]
4. Verify that V X (aẢ) = (Va) XẢ +
aV X Ả where Ả = xyz(x + y + 2)
A
and a = 3xy + 4zx by carrying out
the detailed differentiations.
3. For each of the arrow or quiver
graphs shown below, determine
analytically V°C and V X Č. From
these analytical solutions, identify the
extrema (+/-) and plot these points
on the arrow graph.
(a) C = −✰CosxSiny +
ŷSinxCosy -π<ׂу<π
Ty
(b) C = −xSin2y + ŷCos2y
x, y<π
-π<
(c) C = −xCosx + ŷSiny -π<
x, y < π
Chapter G Solutions
CALCULUS: EARLY TRANS. (LL)W/WEBASSIGN
Ch. G - Prob. 1ECh. G - Refer to Example 1. (a) Find the equation of the...Ch. G - By comparing areas, show that...Ch. G - (a) By comparing areas, show that ln 2 1 ln 3....Ch. G - Prob. 5ECh. G - Prob. 6ECh. G - Prove the third law of exponents for ex [see...Ch. G - Prove the second law of exponents [see (15)].Ch. G - Prove the fourth law of exponents [see (15)].Ch. G - Prob. 10E
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- 7.10 (B/C). A circular flat plate of diameter 305 mm and thickness 6.35 mm is clamped at the edges and subjected to a Uniform lateral pressure of 345 kN/m². Evaluate: (a) the central deflection, (b) the position and magnitude of the maximum radial stress. C6.1 x 10 m; 149.2 MN/m².] 100 200arrow_forward3.15 (B). A beam ABCD is simply supported at B and C with ABCD=2m; BC 4 m. It carries a point load of 60 KN at the free end A, a Uniformly distributed load of 60 KN/m between B and C and an anticlockwise moment of 80 KN m in the plane of the beam applied at the free end D. Sketch and dimension the S.F. and B.M. diagrams, and determine the position and magnitude of the maximum bending moment. CEL.E.] CS.F. 60, 170, 70KN, B.M. 120, +120.1, +80 kNm, 120.1 kNm at 2.83 m to right of 8.7arrow_forward7.1 (A/B). A Uniform I-section beam has flanges 150 mm wide by 8 mm thick and a web 180 mm wide and 8 mm thick. At a certain section there is a shearing force of 120 KN. Draw a diagram to illustrate the distribution of shear stress across the section as a result of bending. What is the maximum shear stress? [86.7 MN/m².arrow_forward
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- 3.10 (A/B). A beam ABCDE is simply supported at A and D. It carries the following loading: a distributed load of 30 kN/m between A and B, a concentrated load of 20 KN at B, a concentrated load of 20 KN at C, a concentrated load of 10 KN at E; a distributed load of 60 kN/m between 0 and E. Span AB = 1.5 BC = CD = DE 1 m. Calculate the value of the reactions at A and D and hence draw the S.F. and B.M. diagrams. What are the magnitude and position of the maximum B.M. on the beam? [41.1, 113.9 KN, 28.15 kNm; 1.37 m from A.J m,arrow_forward3.14 (B). A beam ABCD, 6 m long, is simply-supported at the right-hand end and at a point B Im from the left-hand end A. It carries a vertical load of 10 KN at A, a second concentrated load of 20 KN at C, 3 m from D, and a uniformly distributed load of 10 kN/m between C and D. Determine: (a) the values of the reactions at B and 0, (6) the position and magnitude of the maximum bending moment. [33 KN, 27 KN, 2.7 m from D, 36.45k Nm.]arrow_forward3.17 (B). A simply supported beam has a span of 6 m and carries a distributed load which varies in a linea manner from 30 kN/m at one support to 90 kN/m at the other support. Locate the point of maximum bendin moment and calculate the value of this maximum. Sketch the S.F. and B.M. diagrams. [U.L.] [3.25 m from l.h. end; 272 KN m 30. 90arrow_forward
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