Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 11.1, Problem 23PS
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7.2
Can the level surface x^2 + y^2 + z^2 − 5 = 0 be expressed as the graph of a function f(x, y)?
5. The diagram shows the curve y = 3x – x and tangent to
SPM the curve at point A passes point B.
201
Rajah menunjukkan lengkung y = 3x –x² dan tangen kepada
lengkung pada titik A melalui titik B.
%3D
B(1, 3)
y= 3x-x
(a) Show that h = 2.
Tunjukkan bahawa h = 2.
(b) Calculate the area of the shaded region.
Hitung luas rantau berlorek.
[4]
[4]
Chapter 11 Solutions
Calculus
Ch. 11.1 - Prob. 1PSCh. 11.1 - Prob. 2PSCh. 11.1 - Prob. 3PSCh. 11.1 - Prob. 4PSCh. 11.1 - Prob. 5PSCh. 11.1 - Prob. 6PSCh. 11.1 - Prob. 7PSCh. 11.1 - Prob. 8PSCh. 11.1 - Prob. 9PSCh. 11.1 - Prob. 10PS
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Prob. 3PSCh. 11.6 - Prob. 4PSCh. 11.6 - Prob. 5PSCh. 11.6 - Prob. 6PSCh. 11.6 - Prob. 7PSCh. 11.6 - Prob. 8PSCh. 11.6 - Prob. 9PSCh. 11.6 - Prob. 10PSCh. 11.6 - Prob. 11PSCh. 11.6 - Prob. 12PSCh. 11.6 - Prob. 13PSCh. 11.6 - Prob. 14PSCh. 11.6 - Prob. 15PSCh. 11.6 - Prob. 16PSCh. 11.6 - Prob. 17PSCh. 11.6 - Prob. 18PSCh. 11.6 - Prob. 19PSCh. 11.6 - Prob. 20PSCh. 11.6 - Prob. 21PSCh. 11.6 - Prob. 22PSCh. 11.6 - Prob. 23PSCh. 11.6 - Prob. 24PSCh. 11.6 - Prob. 25PSCh. 11.6 - Prob. 26PSCh. 11.6 - Prob. 27PSCh. 11.6 - Prob. 28PSCh. 11.6 - Prob. 29PSCh. 11.6 - Prob. 30PSCh. 11.6 - Prob. 31PSCh. 11.6 - Prob. 32PSCh. 11.6 - Prob. 33PSCh. 11.6 - Prob. 34PSCh. 11.6 - Prob. 35PSCh. 11.6 - Prob. 36PSCh. 11.6 - Prob. 37PSCh. 11.6 - Prob. 38PSCh. 11.6 - Prob. 39PSCh. 11.6 - Prob. 40PSCh. 11.6 - Prob. 41PSCh. 11.6 - Prob. 42PSCh. 11.6 - Prob. 43PSCh. 11.6 - Prob. 44PSCh. 11.6 - Prob. 45PSCh. 11.6 - Prob. 46PSCh. 11.6 - Prob. 47PSCh. 11.6 - Prob. 48PSCh. 11.6 - Prob. 49PSCh. 11.6 - Prob. 50PSCh. 11.6 - 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- 8. A cam follower roller with radius r is in constant contact with a cam shaped as a triangular right-angle prism with sides a and b (see the next figure). As the cam is moving horizontally, the cam follower is moving vertically along an axis parallel to the Oy axis and at a distance d from it (darrow_forward3. Draw contour maps of each of the following functions, choosing appropriate an appropriate contour interval and showing at least 6 level curves. (a) f(x, y) = x² y² + 4 9 (b) g(x, y) = exp (c) h(x, y) = 3x -y +2.arrow_forward2) Refer to the following plot of some level curves of f(x, y)= c for c = − 1.5, −1, −0.5, 0, 0.5,1, 1.5arrow_forward15.1.77 Find an equation for the family of level surfaces corresponding to f. Describe the level surfaces. f(x,y,z)=sqrtx^2+2z^2 Write an equation for the family of level surfaces where C is constant.arrow_forwardSketch a typical level surface for the function f(x,y,z) = 3x² + 3y² + 3z².arrow_forward22. The tangent line to the graph of y= e–x at the point (3, 1) intersects the x-axis at the point P and the y-axis at the point Q. What is the area of the triangle whose vertices are the origin, point P, and point y%3D Q? (A) 2 (B) 4 (C) 8 (D) 16arrow_forwardfind the local extrema for the following function f(x,y)= x^2 +y^2+xy-7x+4y+9arrow_forward2. Determine the equation of the line tangent to the graph of y = x³ + 2x at the point (1,3). 2.x + 1 3. Determine the equation of the line tangent to the graph of at the point (1, 1). x + 2 4. Determine the equation of the line tangent to the graph of y when r = 9. 2 + VI 5. Assume that f is a differentiable function where f(3) of the line tangent to f when x = 3. 5 and f(3) = 2. Find the equation" 6. Suppose f is a function where the line tangent to it at r = 3 is given by y = 5x + 2. Find the values of f(3) and f'(3). 4 7. Find g'(a) if 9(x) = 8. Let g(x) be a function such that g(2) = -3 and g'(2) = 5. Define f(x) = x2•g(x). Find the value of ((2). (Remember to use the limit definition of the derivative!) 9. Let v(x) be a function such that v(5) = -1 and v'(5) =5. Define u(x) Find the value of u'(5). (Remember to use the limit definition of v(x)" the derivative!)arrow_forward1. Consider the function z = f(x,y) = x2 – 2x + 3y2 + 6y. i. State its domain. ii. Find the range of f. iii. Sketch the level curve of f for z = -4, 0.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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