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 25PS
To determine
To graph :
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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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- 10. Consider a parabola y = x² and a circle with center C(0,2), as shown below. The points A and B are special points where the parabola and circle are mutually tangential. -1 3 2 B (a) Let (x, y) be a point on the parabola, where x 0. Demonstrate the line from (x, y) which also passes through the center of the circle must have a slope of x² - 2 COS I (b) Let (b, b²) be the coordinates of B, the rightmost point of tangency. A special fact about the parabola y = x² is that its slope at a point (x, y) is always given by the formula m = 2x, so at x = b, the slope is 2b. Use this, along with your result from (a) to determine the value of these coordinates of B. Now determine an equation for the tangent line to the circle at B. Also, sketch a picture of this situation. Show your tangent line, the circle, and parabola all on one graph. (d) The normal line through a point is always perpendicular to the tangent line through that same point. Determine an equation for the normal line to the…arrow_forwardSketch the graph of f(x.y) = 4x +y + 1. State the domain and range of the function. Which of the following surface graphs represents f(x,y) = 4x + y? + 1? OA. Ов. OC.arrow_forward19. In the xy-plane the x-axis and the graphs of the lines y=x, y=1 and y+x=4 intersect to form a trapezoid. What is the sum of the slopes of the two nonparallel siges of the trapezoid? (A) -2 (B) -1 (C) 0 (D) 1 (E) 2 Ahmaarrow_forward
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