In Problems 59–64 , use a graphing calculator as necessary to explore the graphs of the indicated cross sections . 63. Let f ( x , y ) = e − ( x 2 + y 2 ) . (A) Explain why f ( a , b ) = f ( c , d ) whenever ( a , b ) and (c, d ) are points on the same circle centered at the origin in the xy plane. (B) Describe the cross sections of the surface z = f ( x , y ) produced by cutting it with the planes x = 0, y = 0, and x = y . (C) Describe the surface z = f ( x , y ).
In Problems 59–64 , use a graphing calculator as necessary to explore the graphs of the indicated cross sections . 63. Let f ( x , y ) = e − ( x 2 + y 2 ) . (A) Explain why f ( a , b ) = f ( c , d ) whenever ( a , b ) and (c, d ) are points on the same circle centered at the origin in the xy plane. (B) Describe the cross sections of the surface z = f ( x , y ) produced by cutting it with the planes x = 0, y = 0, and x = y . (C) Describe the surface z = f ( x , y ).
Solution Summary: The author explains the function of f(a,b) = e- (x2+y), where r radius of the circle is
In Problems 16–27, use the accompanying graph of y = f(x).
16. What is the domain of f?
17. What is the range of f?
(-2, 2)
2
(-6, 2)
18. Find the r-intercept(s), if any, of f.
• (-4, 1)
-4
-2
19. Find the y-intercept(s), if any, of f.
-2
20. Find f(-6) and f(-4).
21. Find lim_f(x).
22. Find lim f(x).
23. Find lim f(x).
24. Find lim f(x).
25. Does lim f(x) exist? If it does, what is it?
26. Is f continuous at 0?
27. Is f continuous at 4?
3. Find the slope of the graph tangent to the curve y = -x* – 2x3 +x that passes
6.
through the point (2, -9)
1. To obtain the graph of y=asinb(x-h)+k, explain what each of the values of a, b, h, and k
affects the graph of function y=sinx.
Chapter 7 Solutions
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY