Sect 14.2 Enhanced Assign

Instructor: Shijun Zheng Course: Spring 2023 - Calculus III (MATH2243-A-B) Student: Jalen Wilson Date: 07/11/24 1. 2 Find Assignment: Sect 14.2 Enhanced Assign 2 2x + 5y − 5 . lim 2 2 (x,y)→( − 4,5) x + y + 2 2 2 2x + 5y − 5 152 lim = 2 2 43 (x,y)→( − 4,5) x + y + 2 ​(Type an integer or a simplified​fraction.) 2. Find the limit. lim csc x tan y (x,y)→(3π/ 2,π/ 4) lim csc x tan y = −1 (x,y)→(3π/ 2,π/ 4) ​(Simplify your answer. Type an exact​answer, using π as​needed.) 3. Find the limit. lim e (x,y)→(ln 7,0) lim e (x,y)→(ln 7,0) x−y 4. x−y = ​(Simplify your answer. Type an integer or a simplified​fraction.) 7 2 lim Find 2 81x − 90xy + 25y by rewriting the fraction first. 9x − 5y (x,y)→(5,9) 9x ≠ 5y 2 2 81x − 90xy + 25y lim 9x − 5y (x,y)→(5,9) = 0 9x ≠ 5y ​(Simplify your​answer.) 5. Perform the indicated operation. Reduce to lowest terms. 3 7t − 28 3 7t − 28 2 − 4−t 2 − 4−t 17 = 7(t − 4) YOU​ANSWERED: 19 7(t − 4) 6. Find the limit by rewriting the fraction first. 22 lim sin x 22 (x,y)→(0,0) x 22 lim (x,y)→(0,0) sin x x 22 22 +y +y 22 22 +y 22 +y = 1 ​(Type an integer or a simplified​fraction.) 7. Find 1 lim P→(5,5, − 1) lim P→(5,5, − 1) 1 x−4 x−4 + 2 + y+3 2 y+3 + + 1 z−3 1 z−3 . = 1 ​(Type an integer or a simplified​fraction.) 8. At what point (x,y) in the plane are the functions below​continuous? a. ​f(x,y) = sin (x + y) 2 2 b. ​f(x,y) = ln x + y − 9 a. Choose the correct answer for points where the function sin (x + y) is continuous. A. for every​(x,y) B. for every​(x,y) such that x ≥ 0 C. for every​(x,y) such that y ≥ 0 D. for every​(x,y) such that x + y > 0 2 2 b. Choose the correct answer for points where the function ln x + y − 9 is continuous. A. for every​(x,y) such that x > 9 and y > 9 B. for every​(x,y) such that x < 9 and y < 9 C. for every​(x,y) such that x2 + y2 > 9 D. for every​(x,y) such that x2 + y2 < 9