Calculus (MindTap Course List)
8th Edition
ISBN: 9781285740621
Author: James Stewart
Publisher: Cengage Learning
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Chapter 4 Solutions
Calculus (MindTap Course List)
Ch. 4.1 - Prob. 1ECh. 4.1 - a Use six rectangles to find estimates of each...Ch. 4.1 - a Estimate the area under the graph of f(x)=1/x...Ch. 4.1 - Prob. 4ECh. 4.1 - Prob. 5ECh. 4.1 - Prob. 6ECh. 4.1 - Prob. 7ECh. 4.1 - Evaluate the upper and lower sums for...Ch. 4.1 - With a programmable calculator or a computer, it...Ch. 4.1 - Prob. 10E
Ch. 4.1 - Some computer algebra systems have commands that...Ch. 4.1 - Prob. 12ECh. 4.1 - The speed of a runner increased steadily during...Ch. 4.1 - The table shows speedometer readings at 10-second...Ch. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - The velocity graph of a braking car is shown. Use...Ch. 4.1 - Prob. 18ECh. 4.1 - In someone infected with measles, the virus level...Ch. 4.1 - The table shows the number of people per day who...Ch. 4.1 - Use Definition 2 to find an expression for the...Ch. 4.1 - Use Definition 2 to find an expression for the...Ch. 4.1 - Use Definition 2 to find an expression for the...Ch. 4.1 - Prob. 24ECh. 4.1 - Determine a region whose area is equal to the...Ch. 4.1 - a Use Definition 2 to find an expression for the...Ch. 4.1 - Prob. 27ECh. 4.1 - Prob. 28ECh. 4.1 - Prob. 29ECh. 4.1 - Prob. 30ECh. 4.1 - Prob. 31ECh. 4.1 - Prob. 32ECh. 4.2 - Evaluate the Riemann sum for f(x)=x1,6x4, with...Ch. 4.2 - If f(x)=cosx0x3/4 evaluate the Riemann sum with n...Ch. 4.2 - If f(x)=x24,0x3, find the Riemann sum with n = 6,...Ch. 4.2 - a Find the Riemann sum for f(x)=1/x,1x2, with four...Ch. 4.2 - The graph of a function f is given. Estimate...Ch. 4.2 - The graph of g is shown. Estimate 24g(x)dx with...Ch. 4.2 - Prob. 7ECh. 4.2 - The table gives the values of a function obtained...Ch. 4.2 - Use the Midpoint Rule with the given value of n to...Ch. 4.2 - Use the Midpoint Rule with the given value of n to...Ch. 4.2 - Use the Midpoint Rule with the given value of n to...Ch. 4.2 - Use the Midpoint Rule with the given value of n to...Ch. 4.2 - If you have a CAS that evaluates midpoint...Ch. 4.2 - With a programmable calculator or computer see the...Ch. 4.2 - Prob. 15ECh. 4.2 - Prob. 16ECh. 4.2 - Prob. 17ECh. 4.2 - Prob. 18ECh. 4.2 - Express the limit as a definite integral on the...Ch. 4.2 - Express the limit as a definite integral on the...Ch. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Use the form of the definition of the integral...Ch. 4.2 - Prob. 24ECh. 4.2 - Prob. 25ECh. 4.2 - Prob. 26ECh. 4.2 - Prove that abxdx=b2a22Ch. 4.2 - Prove that abx2dx=b3a33Ch. 4.2 - Prob. 29ECh. 4.2 - Express the integral as a limit of Riemann sums....Ch. 4.2 - Prob. 31ECh. 4.2 - Express the integral as a limit of sums. Then...Ch. 4.2 - The graph of f is shown. Evaluate each integral by...Ch. 4.2 - The graph of g consists of two straight fines and...Ch. 4.2 - Evaluate the integral by interpreting it in terms...Ch. 4.2 - Evaluate the integral by interpreting it in terms...Ch. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - Evaluate the integral by interpreting it in terms...Ch. 4.2 - Prob. 40ECh. 4.2 - Prob. 41ECh. 4.2 - Given that 0sin4xdx=38, what is 0sin4d?Ch. 4.2 - Prob. 43ECh. 4.2 - Prob. 44ECh. 4.2 - Prob. 45ECh. 4.2 - Prob. 46ECh. 4.2 - Prob. 47ECh. 4.2 - If 28f(x)dx=7.3 and 24f(x)dx=5.9, find 48f(x)dx.Ch. 4.2 - If 09f(x)dx=37 and 09g(x)dx=16, find...Ch. 4.2 - Find 05f(x)dx if f(x)={3forx3xforx3Ch. 4.2 - For the function / whose graph is shown, list the...Ch. 4.2 - If F(x)=2xf(t)dt, where f is the function whose...Ch. 4.2 - Each of the regions A, B, and C bounded by the...Ch. 4.2 - Suppose / has absolute minimum value m and...Ch. 4.2 - Use the properties of integrals to verify the...Ch. 4.2 - Use the properties of integrals to verify the...Ch. 4.2 - Prob. 57ECh. 4.2 - Prob. 58ECh. 4.2 - Prob. 59ECh. 4.2 - Prob. 60ECh. 4.2 - Prob. 61ECh. 4.2 - Use Property 8 of integrals to estimate the value...Ch. 4.2 - Prob. 63ECh. 4.2 - Prob. 64ECh. 4.2 - Use properties of integrals, together with...Ch. 4.2 - Prob. 66ECh. 4.2 - Prob. 67ECh. 4.2 - Prob. 68ECh. 4.2 - Prob. 69ECh. 4.2 - Prob. 70ECh. 4.2 - Let f(x)=0 if x is any rational number and f(x)=1...Ch. 4.2 - Prob. 72ECh. 4.2 - Express the limit as a definite intergal....Ch. 4.2 - Prob. 74ECh. 4.2 - Find 12x2dx. Hint: Choose xi* to be the geometric...Ch. 4.3 - Explain exactly what is meant by the statement...Ch. 4.3 - Let g(x)=0xf(t)dt, where f is the function whose...Ch. 4.3 - Let g(x)=0xf(t)dt, where f is the function whose...Ch. 4.3 - Let g(x)=0xf(t)dt where f is the function whose...Ch. 4.3 - Sketch the area represented by g(x). Then find...Ch. 4.3 - Sketch the area represented by g(x). Then find...Ch. 4.3 - Prob. 7ECh. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Use Part 1 of the Fundamental Theorem of Calculus...Ch. 4.3 - Prob. 16ECh. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - Prob. 19ECh. 4.3 - Evaluate the integral. 11x100dxCh. 4.3 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - Prob. 24ECh. 4.3 - Evaluate the integral. /6sindCh. 4.3 - Evaluate the integral. 55dxCh. 4.3 - Prob. 27ECh. 4.3 - Evaluate the integral. 04(4t)tdtCh. 4.3 - Evaluate the integral. 142+x2xdxCh. 4.3 - Evaluate the integral. 12(3u2)(u+1)duCh. 4.3 - Prob. 31ECh. 4.3 - Evaluate the integral. /4/3csc2dCh. 4.3 - Prob. 33ECh. 4.3 - Evaluate the integral. 12s2+1s2dsCh. 4.3 - Evaluate the integral. 12v5+3v6v4dvCh. 4.3 - Prob. 36ECh. 4.3 - Prob. 37ECh. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - Prob. 40ECh. 4.3 - Prob. 41ECh. 4.3 - Prob. 42ECh. 4.3 - Prob. 43ECh. 4.3 - Prob. 44ECh. 4.3 - Prob. 45ECh. 4.3 - Prob. 46ECh. 4.3 - Evaluate the integral and interpret it as a...Ch. 4.3 - Prob. 48ECh. 4.3 - What is wrong with the equation? 21x4dx=x33]21=38Ch. 4.3 - What is wrong with the equation? 124x3dx=2x2]12=32Ch. 4.3 - Prob. 51ECh. 4.3 - What is wrong with the equation? 0sec2xdx=tanx]0=0Ch. 4.3 - Find the derivative of the function....Ch. 4.3 - Prob. 54ECh. 4.3 - Prob. 55ECh. 4.3 - Prob. 56ECh. 4.3 - Let F(x)=xcosttdt. Find an equation of the tangent...Ch. 4.3 - Prob. 58ECh. 4.3 - On what interval is the curve y=0xt2t2+t+2dt...Ch. 4.3 - Let F(x)=1xf(t)dt, where f is the function whose...Ch. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - The Fresnel function S was defined in Example 3...Ch. 4.3 - The sine integral function Si(x)=0xsinttdt is...Ch. 4.3 - Let g(x)=0xf(t)dt where f is the function whose...Ch. 4.3 - Let g(x)=0xf(t)dt where f is the function whose...Ch. 4.3 - Evaluate the limit by first recognizing the sum as...Ch. 4.3 - Evaluate the limit by first recognizing the sum as...Ch. 4.3 - Prob. 69ECh. 4.3 - Prob. 70ECh. 4.3 - a Show that 11+x31+x3forx0 b Show that...Ch. 4.3 - Prob. 72ECh. 4.3 - Show that 0510x2x4+x2+1dx0.1 by comparing the...Ch. 4.3 - Let f(x)={0ifx0xif0x12xif1x20ifx2 and...Ch. 4.3 - Prob. 75ECh. 4.3 - Prob. 76ECh. 4.3 - A manufacturing company owns a major piece of...Ch. 4.3 - Prob. 78ECh. 4.3 - The following exercises are intended only for...Ch. 4.3 - The following exercises are intended only for...Ch. 4.3 - Prob. 81ECh. 4.3 - Prob. 82ECh. 4.3 - Prob. 83ECh. 4.3 - Prob. 84ECh. 4.4 - Verify by differentiation that the formula is...Ch. 4.4 - Verify by differentiation that the formula is...Ch. 4.4 - Verify by differentiation that the formula is...Ch. 4.4 - Verify by differentiation that the formula is...Ch. 4.4 - Prob. 5ECh. 4.4 - Prob. 6ECh. 4.4 - Find the general indefinite integral....Ch. 4.4 - Prob. 8ECh. 4.4 - Find the general indefinite integral....Ch. 4.4 - Prob. 10ECh. 4.4 - Prob. 11ECh. 4.4 - Prob. 12ECh. 4.4 - Prob. 13ECh. 4.4 - Prob. 14ECh. 4.4 - Find the general indefinite integral....Ch. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.4 - Prob. 19ECh. 4.4 - Prob. 20ECh. 4.4 - Prob. 21ECh. 4.4 - Prob. 22ECh. 4.4 - Prob. 23ECh. 4.4 - Evaluate the integral. 11t(1t)2dtCh. 4.4 - Prob. 25ECh. 4.4 - Prob. 26ECh. 4.4 - Prob. 27ECh. 4.4 - Prob. 28ECh. 4.4 - Prob. 29ECh. 4.4 - Prob. 30ECh. 4.4 - Prob. 31ECh. 4.4 - Prob. 32ECh. 4.4 - Prob. 33ECh. 4.4 - Prob. 34ECh. 4.4 - Prob. 35ECh. 4.4 - Prob. 36ECh. 4.4 - Prob. 37ECh. 4.4 - Prob. 38ECh. 4.4 - Evaluate the integral. 25|x3|dxCh. 4.4 - Prob. 40ECh. 4.4 - Prob. 41ECh. 4.4 - Prob. 42ECh. 4.4 - Use a graph to estimate the x-intercepts of the...Ch. 4.4 - Prob. 44ECh. 4.4 - The area of the region that lies to the right of...Ch. 4.4 - The boundaries of the shaded region in the figure...Ch. 4.4 - Prob. 47ECh. 4.4 - Prob. 48ECh. 4.4 - Prob. 49ECh. 4.4 - A honeybee population starts with 100 bees and...Ch. 4.4 - Prob. 51ECh. 4.4 - Prob. 52ECh. 4.4 - Prob. 53ECh. 4.4 - Prob. 54ECh. 4.4 - The velocity function in meters per second is...Ch. 4.4 - Prob. 56ECh. 4.4 - The acceleration function in m/s2 and the initial...Ch. 4.4 - Prob. 58ECh. 4.4 - Prob. 59ECh. 4.4 - Prob. 60ECh. 4.4 - Prob. 61ECh. 4.4 - Suppose that a volcano is erupting and readings of...Ch. 4.4 - Lake Lanier in Georgia, USA, is a reservoir...Ch. 4.4 - Prob. 64ECh. 4.4 - The graph of the acceleration a(t) of a car...Ch. 4.4 - Shown is the graph of traffic on an Internet...Ch. 4.4 - Prob. 67ECh. 4.4 - Prob. 68ECh. 4.4 - Prob. 69ECh. 4.4 - Prob. 70ECh. 4.4 - Prob. 71ECh. 4.4 - Prob. 72ECh. 4.4 - Prob. 73ECh. 4.4 - The area labeled B is three times the area labeled...Ch. 4.5 - Evaluate the integral by making the given...Ch. 4.5 - Evaluate the integral by making the given...Ch. 4.5 - Prob. 3ECh. 4.5 - Evaluate the integral by making the given...Ch. 4.5 - Prob. 5ECh. 4.5 - Evaluate the integral by making the given...Ch. 4.5 - Prob. 7ECh. 4.5 - Evaluate the indefinite integral. x2sin(x3)dxCh. 4.5 - Prob. 9ECh. 4.5 - Evaluate the indefinite integral. sin1+costdtCh. 4.5 - Evaluate the indefinite integral. sin(2/3)dCh. 4.5 - Evaluate the indefinite integral. sec22dCh. 4.5 - Prob. 13ECh. 4.5 - Evaluate the indefinite integral. y2(4y3)2/3dyCh. 4.5 - Prob. 15ECh. 4.5 - Prob. 16ECh. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Prob. 19ECh. 4.5 - Prob. 20ECh. 4.5 - Prob. 21ECh. 4.5 - Prob. 22ECh. 4.5 - Prob. 23ECh. 4.5 - Prob. 24ECh. 4.5 - Prob. 25ECh. 4.5 - Evaluate the indefinite integral. sec2xtan2xdxCh. 4.5 - Evaluate the indefinite integral. sec3xtanxdxCh. 4.5 - Prob. 28ECh. 4.5 - Evaluate the indefinite integral. x(2x+5)8dxCh. 4.5 - Prob. 30ECh. 4.5 - Evaluate the indefinite integral. Illustrate and...Ch. 4.5 - Prob. 32ECh. 4.5 - Evaluate the indefinite integral. Illustrate and...Ch. 4.5 - Evaluate the indefinite integral. Illustrate and...Ch. 4.5 - Prob. 35ECh. 4.5 - Prob. 36ECh. 4.5 - Evaluate the definite integral. 011+7x3dxCh. 4.5 - Prob. 38ECh. 4.5 - Evaluate the integral. 0/6sintcos2tdtCh. 4.5 - Prob. 40ECh. 4.5 - Evaluate the definite integral. /4/4(x3+x4tanx)dxCh. 4.5 - Prob. 42ECh. 4.5 - Prob. 43ECh. 4.5 - Prob. 44ECh. 4.5 - Prob. 45ECh. 4.5 - Evaluate the definite integral. /3/3x4sinxdxCh. 4.5 - Evaluate the definite integral. 12xx1dxCh. 4.5 - Prob. 48ECh. 4.5 - Evaluate the definite integral. 1/21cos(x2)x3dxCh. 4.5 - Prob. 50ECh. 4.5 - Evaluate the definite integral. 01dx(1+x)4Ch. 4.5 - Prob. 52ECh. 4.5 - Prob. 53ECh. 4.5 - Prob. 54ECh. 4.5 - Prob. 55ECh. 4.5 - Prob. 56ECh. 4.5 - Prob. 57ECh. 4.5 - Prob. 58ECh. 4.5 - Prob. 59ECh. 4.5 - Prob. 60ECh. 4.5 - Prob. 61ECh. 4.5 - If f is continuous function on , prove that...Ch. 4.5 - If a and b are positive numbers, show that...Ch. 4.5 - Prob. 64ECh. 4.5 - Prob. 65ECh. 4.5 - Prob. 66ECh. 4.5 - Prob. 67ECh. 4.5 - Prob. 68ECh. 4.5 - Prob. 69ECh. 4.5 - Prob. 70ECh. 4.5 - Prob. 71ECh. 4.5 - Prob. 72ECh. 4.5 - Prob. 73ECh. 4.5 - Prob. 74ECh. 4.5 - Prob. 75ECh. 4.5 - Prob. 76ECh. 4.5 - Prob. 77ECh. 4.5 - Prob. 78ECh. 4.5 - Prob. 79ECh. 4.5 - Prob. 80ECh. 4.5 - Prob. 81ECh. 4.5 - Prob. 82ECh. 4.5 - Prob. 83ECh. 4.5 - Prob. 84ECh. 4.5 - Prob. 85ECh. 4.R - a Write an expression for a Riemann sum of a...Ch. 4.R - a Write the definition of the definite integral of...Ch. 4.R - Prob. 3CCCh. 4.R - Prob. 4CCCh. 4.R - Prob. 5CCCh. 4.R - Prob. 6CCCh. 4.R - a Explain the meaning of the indefinite integral...Ch. 4.R - Explain exactly what is meant by the statement...Ch. 4.R - State the Substitution Rule. In practice, how do...Ch. 4.R - Prob. 1TFQCh. 4.R - Prob. 2TFQCh. 4.R - Prob. 3TFQCh. 4.R - Prob. 4TFQCh. 4.R - Prob. 5TFQCh. 4.R - Prob. 6TFQCh. 4.R - Prob. 7TFQCh. 4.R - Prob. 8TFQCh. 4.R - Prob. 9TFQCh. 4.R - Prob. 10TFQCh. 4.R - Prob. 11TFQCh. 4.R - Prob. 12TFQCh. 4.R - Prob. 13TFQCh. 4.R - Prob. 14TFQCh. 4.R - Prob. 15TFQCh. 4.R - Prob. 16TFQCh. 4.R - Prob. 17TFQCh. 4.R - Prob. 18TFQCh. 4.R - Use the given graph of f to find the Riemann sum...Ch. 4.R - a Evaluate the Riemann sum for f(x)=x2x0x2 With...Ch. 4.R - Prob. 3ECh. 4.R - Prob. 4ECh. 4.R - Prob. 5ECh. 4.R - Prob. 6ECh. 4.R - Prob. 7ECh. 4.R - Prob. 8ECh. 4.R - The graph of f consists of the three line segments...Ch. 4.R - Prob. 10ECh. 4.R - Prob. 11ECh. 4.R - Prob. 12ECh. 4.R - Prob. 13ECh. 4.R - Prob. 14ECh. 4.R - Prob. 15ECh. 4.R - Prob. 16ECh. 4.R - Prob. 17ECh. 4.R - Prob. 18ECh. 4.R - Evaluate the integral, if it exists. 15dt(t4)2Ch. 4.R - Prob. 20ECh. 4.R - Prob. 21ECh. 4.R - Prob. 22ECh. 4.R - Prob. 23ECh. 4.R - Prob. 24ECh. 4.R - Prob. 25ECh. 4.R - Prob. 26ECh. 4.R - Prob. 27ECh. 4.R - Prob. 28ECh. 4.R - Evaluate the integral, if it exists. 03|x24|dxCh. 4.R - Prob. 30ECh. 4.R - Prob. 31ECh. 4.R - Prob. 32ECh. 4.R - Prob. 33ECh. 4.R - Prob. 34ECh. 4.R - Prob. 35ECh. 4.R - Prob. 36ECh. 4.R - Prob. 37ECh. 4.R - Find the derivative of the function....Ch. 4.R - Find the derivative of the function. y=xxcosdCh. 4.R - Prob. 40ECh. 4.R - Prob. 41ECh. 4.R - Prob. 42ECh. 4.R - Prob. 43ECh. 4.R - Prob. 44ECh. 4.R - Prob. 45ECh. 4.R - Prob. 46ECh. 4.R - Prob. 47ECh. 4.R - Prob. 48ECh. 4.R - Prob. 49ECh. 4.R - Let f(x)={x1if3x01x2if0x1 Evaluate 31f(x)dx by...Ch. 4.R - Prob. 51ECh. 4.R - The Fresnel function S(x)=0xsin(12t2)dt was...Ch. 4.R - Prob. 53ECh. 4.R - Prob. 54ECh. 4.R - Prob. 55ECh. 4.R - Find limh01h22+h1+t3dtCh. 4.R - Prob. 57ECh. 4.R - Prob. 58ECh. 4.P - If xsinxx=0x2f(t)dt, where f is a continuous...Ch. 4.P - Prob. 2PCh. 4.P - If f is a differentiable function such that f(x)...Ch. 4.P - Prob. 4PCh. 4.P - Prob. 5PCh. 4.P - Prob. 6PCh. 4.P - Prob. 7PCh. 4.P - Prob. 8PCh. 4.P - Prob. 9PCh. 4.P - Prob. 10PCh. 4.P - Suppose the coefficients of the cubic polynomial...Ch. 4.P - Prob. 12PCh. 4.P - Prob. 13PCh. 4.P - The figure shows a parabolic segment, that is, a...Ch. 4.P - Given the point a, b in the first quadrant, find...Ch. 4.P - The figure shows a region consisting of all points...Ch. 4.P - Prob. 17PCh. 4.P - For any number c, we let fc(x) be the smaller of...
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- 2:21 MM -8 -7 -6 -5 -4 0 5 4 3 2 N -3 -4 +5 +6 5G 100% Identify the function whose graph appears above. f(x) = = tan X 3 ✓ Question Help: ☐ Video ☐ Message instructor Submit Question |||arrow_forward4 3. 2. 1 0 Π 元 -1 3 x -53. 5π 2π The graph of the function y = f(x) is shown in the xy-plane. Which of the following is the graph of the polar function r = f(e) in the polar coordinate system? A B Polar axis Polar axis Polar axis Polar axisarrow_forward٣:٥٣ 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 ) 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 + - ) ،…arrow_forward
- 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…arrow_forward2. Symmetry Evaluate the following integrals using symmetry argu- ments. Let R = {(x, y): -a ≤ x ≤ a, −b ≤ y ≤ b}, where a and b are positive real numbers. a. SS Sf xye xye¯(x² + y²) dA R b. C sin (x − y) - dA x² + y² + 1 Rarrow_forwardChoose a convenient order When converted to an iterated integral, the following double integrals are easier to evaluate in one order please show all stepsarrow_forward
- The graph of f' is below. Use it to determine where the local minima and maxima for f are. If there are multiple answers, separate with commas. 2 f'(x) N -5 -4 3-2-1 -1 -2 -3 -4 12 3 4 5 -x Local minima at x Local maxima at xarrow_forwardThe graph of f' is below. Use it to determine the intervals where f is increasing. -5-4-32 4- 3 2 1 -2 -3 +x 2 3 4 5arrow_forwardThe graph of f' is below. Use it to determine where the inflection points are and the intervals where f is concave up and concave down. If there are multiple inflection points, separate with a comma. 6 5 4 3 2 1 f'(x) +x -6-5-4-3 -2 -1 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6+ Inflection point(s) at x = Concave up: Concave down:arrow_forward
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