Thomas' Calculus (14th Edition)
14th Edition
ISBN: 9780134438986
Author: Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher: PEARSON
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Chapter 13, Problem 6PE
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النموذج الاول
. . .
O O O
بشما ند الحمر الحمر
الجمهورية الجنية
وزارة التربية والتعليم
اليوم
التاريخ
اللجنة العليا للاختبارات
الزمن
اختبار مادة الجبر والهندسة
لجنة المطابع السرية المركزية
للشهادة الثانوية العامة (القسم العلمي)
الفترة
%97
(1)
ظلل في ورقة الإجابة الدائرة التي تحتوي على الحرف ( ص ) للإجابة الصحيحة والحرف ( خ ) للإجابة الخطأ بحسب رقم الفقرة لكل مما يأتي ( درجة لكل فقرة )
)1
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2
)
3
)
4
) بؤرة القطع س" = ١٢ ص هي (
۲
) طول المحور الأصغر للقطع ٩ س + ص = ٩ يساوي 6 وحدات طول .
) إذا كان & عدد مركب ، 181 + 11 = ٦ ، فإن ١١ = ٣ .
) إذا كان م + ۳ ت = ۲ + ت ب م ، ب دع ، فإن م + ب =
5 ( ) إذا كان & = ۱ + ٣ ت ، فإن ٠ = ١٠ .
6 ( - ) إذا كان ٥٠ - ٣ - ١٢٠ ٤ - ٣ ، فإن قيمة ٧ = ٥ .
1
)
=
N
) إذا كان ح هو الحد الخالي من س في المفكوك ( س +
v. N
8 ( ( قيمة المقدار , = + ۱ ، * . . +
، فإن قيمة ٧ = ١٦ .
۱ +
9 ( ) المستقيمان المقاربان للقطع الذي معادلته س" = ١ هما ص = :
۹
10 ( ) إذا كان ٥ + س = ٢٤ ، فإن قيمة س = - 1
س
11 ( ) إذا كانت النسبة بين الحدين الأوسطين تساوي 9 في المفكوك ( س + - ) ،…
الاسم
يمنع استخدام الآلة الحاسبة
ظلل في ورقة الإجابة الدائرة التي تحتوي على الحرف (ص) للإجابة الصحيحة والحرف (خ) للإجابة الخطأ بحسب رقم الفقرة لكل مما يأتي:
درجة لكل فقرة.
( ) نها جا
元
جتا
= صفر
س ۱
س
س -۱
( ) يمكن إعادة تعريف الدالة د(س) = س قاس لكي تكون متصلة عند س = 7
( ) إذا كانت د(س) = (٢) س - س ) ؛ فإن د(١) = ٦
٢ س ص ( ) إذا كانت س +
0=
؛ فإن عند ) - ١ ، - ٦ ) تساوي (٦)
( ) إذا كانت د(س) = س ه ، و (س) = ٣ س ٢ + ٢ س ؛ فإن ( د ) (۱) = ۸
) ( معادلة ناظم الدالة ص = د(س) عند النقطة ) ( ، د (۲)) هي ص - (د (م) - - د (۲) ( س - م )
( ) إذا كانت ص = ظتا٢ س ؛ فإن ص = ٢ ص قتا ٢س
) ( إذا كانت د(س) = س ؛ فإن د (T) =
جتاس
1-
T
( ) إذا كانت د(س) = 1 - جناس
جاس
؛ فإن د () = - 1
( ) إذا كانت الدالة د (س) تحقق شروط مبرهنة القيمة المتوسطة على [ ، ب ] ، فإنه يوجد جـ ] ، ب [ بحيث (جـ) =
(P) + (~)- -
ب + P
1
2
3
4
5
6
7
8
9
10
11
( ) للدالة د(س) = لو ( س ) + (٣) نقطة حرجة عند س = .
( ) إذا كان س = - ٢ مقارباً رأسياً للدالة د(س)
12
10 13
14
15
16
17
س = لو|س | + ث
-
=
۲ س + ٣
ب س + ٤ ، فإن معادلة…
Chapter 13 Solutions
Thomas' Calculus (14th Edition)
Ch. 13.1 - In Exercises 1–4, find the given limits.
1.
Ch. 13.1 - In Exercises 1–4, find the given limits.
2.
Ch. 13.1 - In Exercises 1–4, find the given limits.
3.
Ch. 13.1 - In Exercises 1–4, find the given limits.
4.
Ch. 13.1 - Motion in the Plane
In Exercises 5–8, r(t) is the...Ch. 13.1 - Motion in the Plane
In Exercises 5–8, r(t) is the...Ch. 13.1 - In Exercises 5–8, r(t) is the position of a...Ch. 13.1 - In Exercises 5–8, r(t) is the position of a...Ch. 13.1 - Prob. 9ECh. 13.1 - Prob. 10E
Ch. 13.1 - Exercises 9–12 give the position vectors of...Ch. 13.1 - Prob. 12ECh. 13.1 - In Exercises 13–18, r(t) is the position of a...Ch. 13.1 - In Exercises 13–18, r(t) is the position of a...Ch. 13.1 - In Exercises 13–18, r(t) is the position of a...Ch. 13.1 - In Exercises 13–18, r(t) is the position of a...Ch. 13.1 - In Exercises 13–18, r(t) is the position of a...Ch. 13.1 - In Exercises 13–18, r(t) is the position of a...Ch. 13.1 - In Exercises 19–22, r(t) is the position of a...Ch. 13.1 - In Exercises 19–22, r(t) is the position of a...Ch. 13.1 - In Exercises 19–22, r(t) is the position of a...Ch. 13.1 - Prob. 22ECh. 13.1 - As mentioned in the text, the tangent line to a...Ch. 13.1 - Tangents to Curves
As mentioned in the text, the...Ch. 13.1 - Tangents to Curves
As mentioned in the text, the...Ch. 13.1 - Tangents to Curves
As mentioned in the text, the...Ch. 13.1 - In Exercises 27-30, find the value(s) of t so that...Ch. 13.1 - In Exercises 27-30, find the value(s) of t so that...Ch. 13.1 - In Exercises 27-30, find the value(s) of t so that...Ch. 13.1 - In Exercises 27-30, find the value(s) of t so that...Ch. 13.1 - In Exercises 31–36, r(t) is the position of a...Ch. 13.1 - In Exercises 31–36, r(t) is the position of a...Ch. 13.1 - In Exercises 31–36, r(t) is the position of a...Ch. 13.1 - In Exercises 31–36, r(t) is the position of a...Ch. 13.1 - Prob. 35ECh. 13.1 - In Exercises 31–36, r(t) is the position of a...Ch. 13.1 - Motion along a circle Each of the following...Ch. 13.1 - Motion along a circle Show that the vector-valued...Ch. 13.1 - Motion along a parabola A particle moves along the...Ch. 13.1 - Motion along a cycloid A particle moves in the...Ch. 13.1 - Let r be a differentiable vector function of t....Ch. 13.1 - Prob. 42ECh. 13.1 - Prob. 43ECh. 13.1 - Prob. 44ECh. 13.1 - Prob. 45ECh. 13.1 - Limits of cross products of vector functions...Ch. 13.1 - Differentiable vector functions are continuous...Ch. 13.1 - Constant Function Rule Prove that if u is the...Ch. 13.2 - Evaluate the integrals in Exercises 1–10.
1.
Ch. 13.2 - Evaluate the integrals in Exercises 1–10.
2.
Ch. 13.2 - Evaluate the integrals in Exercises 1–10.
3.
Ch. 13.2 - Evaluate the integrals in Exercises 1–10.
4.
Ch. 13.2 - Evaluate the integrals in Exercises 1–10.
5.
Ch. 13.2 - Evaluate the integrals in Exercises 1–10.
6.
Ch. 13.2 - Evaluate the integrals in Exercises 1–10.
7.
Ch. 13.2 - Prob. 8ECh. 13.2 - Evaluate the integrals in Exercises 1–10.
9.
Ch. 13.2 - Evaluate the integrals in Exercises 1–10.
10.
Ch. 13.2 - Solve the initial value problems in Exercises...Ch. 13.2 - Solve the initial value problems in Exercises...Ch. 13.2 - Solve the initial value problems in Exercises...Ch. 13.2 - Solve the initial value problems in Exercises...Ch. 13.2 - Solve the initial value problems in Exercises...Ch. 13.2 - Solve the initial value problems in Exercises...Ch. 13.2 - Solve the initial value problems in Exercises...Ch. 13.2 - Solve the initial value problems in Exercises...Ch. 13.2 - Solve the initial value problems in Exercises...Ch. 13.2 - Solve the initial value problems in Exercises...Ch. 13.2 - At time t = 0, a particle is located at the point...Ch. 13.2 - Prob. 22ECh. 13.2 - Travel time A projectile is fired at a speed of...Ch. 13.2 - Range and height versus speed
Show that doubling a...Ch. 13.2 - Flight time and height A projectile is fired with...Ch. 13.2 - Throwing a baseball A baseball is thrown from the...Ch. 13.2 - Firing golf balls A spring gun at ground level...Ch. 13.2 - Prob. 28ECh. 13.2 - Equal-range firing angles What two angles of...Ch. 13.2 - Prob. 30ECh. 13.2 - Prob. 31ECh. 13.2 - Colliding marbles The accompanying figure shows an...Ch. 13.2 - Firing from (x0, y0) Derive the equations
(see...Ch. 13.2 - Where trajectories crest For a projectile fired...Ch. 13.2 -
Launching downhill An ideal projectile is...Ch. 13.2 - Prob. 36ECh. 13.2 - Prob. 37ECh. 13.2 - Prob. 38ECh. 13.2 - Prob. 39ECh. 13.2 - The view from Skylab 4 What percentage of Earth’s...Ch. 13.2 - Solve the initial value problems in Exercises...Ch. 13.2 - Hitting a baseball with linear drag Consider the...Ch. 13.2 - Prob. 43ECh. 13.2 - Products of scalar and vector functions Suppose...Ch. 13.2 - Antiderivatives of vector functions
Use Corollary...Ch. 13.2 - The Fundamental Theorem of Calculus The...Ch. 13.2 -
Hitting a baseball with linear drag under a wind...Ch. 13.2 - Prob. 48ECh. 13.3 - In Exercises 1–8, find the curve’s unit tangent...Ch. 13.3 - In Exercises 1–8, find the curve’s unit tangent...Ch. 13.3 - In Exercises 1–8, find the curve’s unit tangent...Ch. 13.3 - In Exercises 1–8, find the curve’s unit tangent...Ch. 13.3 - In Exercises 1–8, find the curve’s unit tangent...Ch. 13.3 - In Exercises 1–8, find the curve’s unit tangent...Ch. 13.3 - In Exercises 1–8, find the curve’s unit tangent...Ch. 13.3 - In Exercises 1–8, find the curve’s unit tangent...Ch. 13.3 - Find the point on the curve
at a distance 26...Ch. 13.3 -
Find the point on the curve
r(t) = (12 sin t)i −...Ch. 13.3 - In Exercises 11–14, find the arc length parameter...Ch. 13.3 - In Exercises 11–14, find the arc length parameter...Ch. 13.3 - In Exercises 11–14, find the arc length parameter...Ch. 13.3 - In Exercises 11–14, find the arc length parameter...Ch. 13.3 - Arc length Find the length of the curve
from (0,...Ch. 13.3 - Length of helix The length of the turn of the...Ch. 13.3 - Length is independent of parametrization To...Ch. 13.3 - The involute of a circle If a siring wound around...Ch. 13.3 - (Continuation of Exercise 19.) Find the unit...Ch. 13.3 - Prob. 21ECh. 13.3 - Prob. 22ECh. 13.4 - Find T, N, and κ for the plane curves in Exercises...Ch. 13.4 - Find T, N, and κ for the plane curves in Exercises...Ch. 13.4 - Prob. 3ECh. 13.4 - Find T, N, and κ for the plane curves in Exercises...Ch. 13.4 - A formula for the curvature of the graph of a...Ch. 13.4 - A formula for the curvature of a parametrized...Ch. 13.4 -
Normals to plane curves
Show that n(t) = −g′(t)i...Ch. 13.4 - (Continuation of Exercise 7.)
Use the method of...Ch. 13.4 - Find T, N, and κ for the space curves in Exercises...Ch. 13.4 - Find T, N, and κ for the space curves in Exercises...Ch. 13.4 - Find T, N, and κ for the space curves in Exercises...Ch. 13.4 - Find T, N, and κ for the space curves in Exercises...Ch. 13.4 - Find T, N, and κ for the space curves in Exercises...Ch. 13.4 - Find T, N, and κ for the space curves in Exercises...Ch. 13.4 - Find T, N, and κ for the space curves in Exercises...Ch. 13.4 - Find T, N, and κ for the space curves in Exercises...Ch. 13.4 - Show that the parabola , has its largest curvature...Ch. 13.4 - Show that the ellipse x = a cos t, y = b sin t, a...Ch. 13.4 - Maximizing the curvature of a helix In Example 5,...Ch. 13.4 - Prob. 20ECh. 13.4 - Find an equation for the circle of curvature of...Ch. 13.4 - Find an equation for the circle of curvature of...Ch. 13.4 - Prob. 23ECh. 13.4 - Prob. 24ECh. 13.4 - Prob. 25ECh. 13.4 - Prob. 26ECh. 13.4 - Prob. 27ECh. 13.4 - Prob. 28ECh. 13.4 - Osculating circle Show that the center of the...Ch. 13.4 - Osculating circle Find a parametrization of the...Ch. 13.5 - In Exercises 1 and 2, write a in the form a = aTT...Ch. 13.5 - In Exercises 1 and 2, write a in the form a = aTT...Ch. 13.5 - In Exercises 3–6, write a in the form a = aTT +...Ch. 13.5 - In Exercises 3–6, write a in the form a = aTT +...Ch. 13.5 - In Exercises 3–6, write a in the form a = aTT +...Ch. 13.5 - In Exercises 3–6, write a in the form a = aTT +...Ch. 13.5 - In Exercises 7 and 8, find r, T, N, and B at the...Ch. 13.5 - In Exercises 7 and 8, find r, T, N, and B at the...Ch. 13.5 - In Exercises 9–16 of Section 13.4, you found T, N,...Ch. 13.5 - Prob. 10ECh. 13.5 - In Exercises 9–16 of Section 13.4, you found T, N,...Ch. 13.5 - In Exercises 9–16 of Section 13.4, you found T, N,...Ch. 13.5 - In Exercises 9–16 of Section 13.4, you found T, N,...Ch. 13.5 - Prob. 14ECh. 13.5 - In Exercises 9–16 of Section 13.4, you found T, N,...Ch. 13.5 - In Exercises 9–16 of Section 13.4, you found T, N,...Ch. 13.5 - Prob. 17ECh. 13.5 - Prob. 18ECh. 13.5 - Prob. 19ECh. 13.5 - Prob. 20ECh. 13.5 - Prob. 21ECh. 13.5 - Prob. 22ECh. 13.5 - A sometime shortcut to curvature If you already...Ch. 13.5 - What can be said about the torsion of a smooth...Ch. 13.5 - Differentiable curves with zero torsion lie in...Ch. 13.5 - A formula that calculates τ from B and v If we...Ch. 13.6 - In Exercises 1–7, find the velocity and...Ch. 13.6 - In Exercises 1–7, find the velocity and...Ch. 13.6 - In Exercises 1–7, find the velocity and...Ch. 13.6 - In Exercises 1–7, find the velocity and...Ch. 13.6 - In Exercises 1–7, find the velocity and...Ch. 13.6 - In Exercises 1–7, find the velocity and...Ch. 13.6 - Prob. 7ECh. 13.6 - Prob. 8ECh. 13.6 - Circular orbits Show that a planet in a circular...Ch. 13.6 - Prob. 10ECh. 13.6 - Prob. 11ECh. 13.6 - Do the data in the accompanying table support...Ch. 13.6 - Prob. 13ECh. 13.6 - Prob. 14ECh. 13.6 - Prob. 15ECh. 13.6 - Prob. 16ECh. 13.6 - Prob. 17ECh. 13.6 - Prob. 18ECh. 13 - Prob. 1GYRCh. 13 - How do you define and calculate the velocity,...Ch. 13 - Prob. 3GYRCh. 13 - Prob. 4GYRCh. 13 - Prob. 5GYRCh. 13 - Prob. 6GYRCh. 13 - Prob. 7GYRCh. 13 - Define curvature, circle of curvature (osculating...Ch. 13 - Prob. 9GYRCh. 13 - Prob. 10GYRCh. 13 - Prob. 11GYRCh. 13 - Prob. 12GYRCh. 13 - Prob. 13GYRCh. 13 - In Exercises 1 and 2, graph the curves and sketch...Ch. 13 - Prob. 2PECh. 13 - Prob. 3PECh. 13 - Prob. 4PECh. 13 - Finding curvature At point P, the velocity and...Ch. 13 - Prob. 6PECh. 13 - Prob. 7PECh. 13 - Prob. 8PECh. 13 - Prob. 9PECh. 13 - Speed along a cycloid A circular wheel with radius...Ch. 13 - Prob. 11PECh. 13 - Javelin A javelin leaves the thrower’s hand 7 ft...Ch. 13 - Prob. 13PECh. 13 - Javelin In Potsdam in 1988, Petra Felke of (then)...Ch. 13 - Prob. 15PECh. 13 - Find the lengths of the curves in Exercises 15 and...Ch. 13 - Prob. 17PECh. 13 - Prob. 18PECh. 13 - In Exercises 17-20, find T, N, B, and k at the...Ch. 13 - Prob. 20PECh. 13 - In Exercises 21 and 22, write a in the form a =...Ch. 13 - Prob. 22PECh. 13 - Prob. 23PECh. 13 - Prob. 24PECh. 13 - Prob. 25PECh. 13 - Prob. 26PECh. 13 - Find parametric equations for the line that is...Ch. 13 - Find parametric equations for the line that is...Ch. 13 - Prob. 29PECh. 13 - Prob. 30PECh. 13 - Prob. 31PECh. 13 - The view from Skylab 4 What percentage of Earth’s...Ch. 13 - Prob. 1AAECh. 13 - Suppose the curve in Exercise 1 is replaced by the...Ch. 13 - Prob. 3AAECh. 13 - Prob. 4AAECh. 13 - Prob. 5AAECh. 13 - Express the curvature of a twice-differentiable...Ch. 13 - Prob. 7AAECh. 13 - Prob. 8AAECh. 13 - Unit vectors for position and motion in...
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