HW1
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HW1

Course Number: PHYSICS PHYS 110, Spring 2010

College/University: Middle East Technical...

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lume, inside of a positively charged conducting sphere. 10) Which of the following statements about Gauss's law are correct? (There may be more than one correct choice.) A) The electric flux passing through a Gaussian surface depends only on the amount of charge inside that surface, not on its size or shape. B) Gauss's law is valid only for symmetric charge distributions, such as spheres and cylinders. C) If there...

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inside lume, of a positively charged conducting sphere. 10) Which of the following statements about Gauss's law are correct? (There may be more than one correct choice.) A) The electric flux passing through a Gaussian surface depends only on the amount of charge inside that surface, not on its size or shape. B) Gauss's law is valid only for symmetric charge distributions, such as spheres and C) cylinders. If there is no charge inside of a Gaussian surface, the electric field must be zero at points of that surface. D) If a Gaussian surface is completely inside an electrostatic conductor, the electric field must always be zero at all points on that surface. E) Only charge enclosed within a Gaussian surface can produce an electric field at points on that surface. 9) 10) 4

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Middle East Technical University - PHYSICS - PHYS 110
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Middle East Technical University - PHYSICS - PHYS 110
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Middle East Technical University - PHYSICS - PHYS 110
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Middle East Technical University - PHYSICS - PHYS 110
Middle East Technical University - PHYSICS - PHYS 110
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Alpha particles (charge = +2e, mass = 6.68 10-27 kg) are accelerated in a cyclotron to a final orbit radius of 0.60 m. The magnetic field in the cycl
Middle East Technical University - PHYSICS - PHYS 110
Middle East Technical University - MATHEMATIC - MATH 119
MATH 120RECITATION QUESTIONS (WEEK 1)1. Determine whether the sequence converges or diverges.If it converges,find the limit. a) an = (-1)n n3 n3 + 2n2 + 1 ln n b) an = ln 2n n! c) an = n 22. Use a graph of the sequence to decide whether the sequence is
Middle East Technical University - MATHEMATIC - MATH 119
MATH 120RECITATION QUESTIONS WEEK 21. Use the integral test to show thatn=0 e-n converges.22. Show thatn=21 converges if and only if p > 1. n(ln n)p3. Does the seriesn=2ln n n23converge? 1 1 - sin ) converges or diverges. n n4. Determine whe
Middle East Technical University - MATHEMATIC - MATH 119
MATH 120RECITATION QUESTIONS WEEK 31. Find the radius of convergence and interval of convergence of the series.a)n=1 xn 5n n5 xn (ln n)nb)n=22. A function f is defined by f (x) = 1 + 2x + x2 + 2x3 + x4 + that is, its coefficients are c2n = 1 and c
Middle East Technical University - MATHEMATIC - MATH 119
MATH 120RECITATION QUESTIONS WEEK 41. Find the Maclaurin series for f (x) = (1 + x)-3 , and the radius and interval of convergence, also. 2. Find the Maclaurin series of f (x) = cos x2 and its radius of convergence. Compare the graph of f and those of i
Middle East Technical University - MATHEMATIC - MATH 119
MATH 120WEEK 5 (RECITATION QUESTIONS)1. Find an equation of the sphere that passes through the point (4, 3, -1) and has center (3, 8, 1). 2. Describe in words the region of3represented by the equation x2 + y 2 = 1. 33. If v lies in the first quadran
Middle East Technical University - MATHEMATIC - MATH 119
MATH 120WEEK 6 (RECITATION QUESTIONS)1. Reduce the equation 4y 2 + z 2 - x - 16y - 4z + 20 = 0 to one of the standard forms, classify the surface, and sketch it. 2. Sketch the region bounded by the surfaces z = x2 + y 2 and x2 + y 2 = 1 for 1 z 2.3. Fi
Middle East Technical University - MATHEMATIC - MATH 119
MATH 120RECITATION QUESTIONS (WEEK 7)1. Using different directions to approach the origin, show that the following limits do not exist. a) b) lim(x,y)(0,0)xy x2 + y 2xy 2 (x,y)(0,0) x2 + y 4 lim2. Using the formal definition of the limit prove a) b)
Middle East Technical University - MATHEMATIC - MATH 119
MATH 120RECITATION QUESTIONS (WEEK 8)1. Find an equation of the tangent plane to the given surface at the specified point. a) z = b) z = e 4 - x2 - 2y 2 ,x2 -y 2(1, -1, 1),(1, -1, 1)2. Explain why the function f (x, y) =x is differentiable at the
Middle East Technical University - MATHEMATIC - MATH 119
MATH 120RECITATION QUESTIONS (WEEK 9)1. Let f (x, y) =2xy x2 +y 2if (x, y) = (0, 0) 0 if (x, y) = (0, 0)Show that Du f (0, 0) exists in every direction u = cos, sin , 0 2, but the formula Du f (0, 0) = f (0, 0) u is true only for u = i or u = j . 2.
Middle East Technical University - MATHEMATIC - MATH 119
INTEGRATION PROBLEMS, MATH 120, WEEK 10DAVID PIERCE1. FindRf when R = [0, 2] [1, 2] and f (x, y) = 3xy 2 - 2x2 y. x 1 and 0 y 1.2. Find the average value of y 2 /(x2 + 1) when 03. Express as an iterated integral the volume enclosed by: the two sheet
Middle East Technical University - MATHEMATIC - MATH 119
MATH 120WEEK 11 (RECITATION QUESTIONS)1 + cos . 21. Find the area inside the larger loop and outside the smaller loop of the limacons r =2. Find the volume of the solid bounded by the cylinders x2 + y 2 = r2 and y 2 + z 2 = r2 . 3. Use polar coordinat
Middle East Technical University - MATHEMATIC - MATH 119
MATH 120WEEK 12 (RECITATION QUESTIONS)1. Find the area of the surface : the part of the plane z = 2 + 3x + 4y that lies above the rectangle [0, 5] [1, 4]. 2. Find the area of the surface : the part of the sphere x2 + y 2 + z 2 = 4z that lies inside the
Middle East Technical University - MATHEMATIC - MATH 119
MATH 120 SPRING 2008 WEEK 13 RECITATION (1) Plot the gradient vector fields and level curves of the functions given below: (a) f (x, y) = x2 - y 2 (b) f (x, y) = + x2 + y 2 (2) Evaluate xy 2 dsCwhere C is given by r(t) = (cos t, t, sin t). (3) Evaluate
Middle East Technical University - MATHEMATIC - MATH 119
MATH 120WEEK 14 (RECITATION QUESTIONS)1. Determine whether or not F(x, y) = (x3 + 4xy)i + (4xy - y 3 )j is a conservative vector field.If it is, find a function f such that F = f 2. (a) Find a function f such that F = (b) Use part (a) to evaluate where
Middle East Technical University - MATHEMATIC - MATH 119
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Middle East Technical University - MATHEMATIC - MATH 119
Math120 Recitation 3October 4, 20061. Let f (x) = 4 - x2 x-1 if x 2, if x > 2.(a) Find limx2- f (x) and limx2+ f (x). (b) Does limx2 f (x) exists? (c) Sketch the graph of f . 2. Show by means of an example that limxa f (x)g(x) may exists even though ne
Middle East Technical University - MATHEMATIC - MATH 119
Math119 Recitation 5October 18, 20061. Find a formula for f n (x) for f (x) = (1 + x)-1 . 2. Find the given derivative by observing the pattern f 35 (x); where f (x) = x sin x 3. Find constants A, B, C such that the function y = Ax2 + Bx + C satisfies t
Middle East Technical University - MATHEMATIC - MATH 119
Math 119 Recitation 6October 21, 20061. Evaluate the following limits or explain why they do not exist.|x-2| (a) limx2 |x|-2 . (b) Let 5 - x2 f (x) 5 - x3 for -1 x 1. Find limx0 f (x).(c) limx11-x3 . 1- x(d) limx (e) (f)x+sin x 2x+7-5 sin x . x+x l
Middle East Technical University - MATHEMATIC - MATH 119
Math 119 Recitation 7November 1, 20061. Verify that the function f (x) = sin(2x) satisfies (a) f is continuous on [-1, 1], (b) f is differentiable on (-1, 1), (c) f (-1) = f (1). and find all numbers c (-1, 1) such that f (c) = 0. 2. Verify that the fun
Middle East Technical University - MATHEMATIC - MATH 119
Math 119 Recitation 8November 6, 20061. Find the dimensions of the isoceles triangle of largest area that can be inscribed in a circle of radius r. 2. A right circular cylinder is inscribed in a sphere of radius r. Find the largest possible surface area
Middle East Technical University - MATHEMATIC - MATH 119
Math 119 Recitation 9November 16, 20061. Use mid-point rule to approximate 2. Express the limit limnn i=1 5 x-1 dx 1 x+1with n = 4.xi sin xi x on [0, ] as a definite integral.5 (1 -13. Use formal definition of integral to evaluate 4. Prove thatb a
Middle East Technical University - MATHEMATIC - MATH 119
Math 119 Recitation 10November 21, 20061. Find the area of the region bounded by y 2 = 2x and x - y = 4. 2. Let R be the region between the parabolas y = x2 and y = 8x. (a) Find the area of R. (b) Find the volume of the solid of revolution that we obtai
Middle East Technical University - MATHEMATIC - MATH 119
Math 119 Recitation 12December 5, 20061. Differentiate (a) y = arcsin 1 - x2 (b) y = arctan 1-x 1+x (c) y = arctan (sin x) (d) y = tanh (ln x) 2. Find the tangent line to the curve arctan ( 2x ) - x = 0 at the point (1, 2). y y2 3. Evaluate the integral
Middle East Technical University - MATHEMATIC - MATH 119
Math 119 Recitation 13December 20, 20061. Investigate the convergence using the comparison and limit comparison tests (a) (b)1 dx 0 (1-x3 ) x2 +x4 5 dx 2 (x-3)2 (x-2)3/22. Use the limit and the comparison tests to deterimine the convergence of the fol
Middle East Technical University - MATHEMATIC - MATH 119
MATH-119WEEK 6 RECITATION QUESTIONS1. Given that the graph of f passes through the point (1, 6) and that the slope of its tangent line at (x, f (x) is 2x + 1,find f (2) 2. The graph of the velocity function of a car is shown in the figure.Sketch the gra
Middle East Technical University - MATHEMATIC - MATH 119
MATH-119 WEEK 11 RECITATION QUESTIONS Evaluate the integrals 1. x arctan xdx./42.0x sec2 xdx. x4 (ln x)2 dx23. 4.1x2 dx . 9 - x25.dx . 6x - x2 - 8 ex e2x - 1 dx.ln 36.ln 27.sin2 x cot3 xdx./68.0cos x sec(2x)dx. x2 ex dx39.andx3 ex
Middle East Technical University - MATHEMATIC - MATH 119
Middle East Technical University - MATHEMATIC - MATH 119
Middle East Technical University - MATHEMATIC - MATH 119
Middle East Technical University - MATHEMATIC - MATH 119
Middle East Technical University - MATHEMATIC - MATH 119
Middle East Technical University - MATHEMATIC - MATH 119
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Middle East Technical University - MATHEMATIC - MATH 119
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Middle East Technical University - MATHEMATIC - MATH 119
Middle East Technical University - MATHEMATIC - MATH 119
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Middle East Technical University - MATHEMATIC - MATH 119
Middle East Technical University - MATHEMATIC - MATH 119
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