D2L Units - CHMI 2220EL 10-Clinic: x *Course Hero X MATH_1036_Assignment 1_20 x Al Chatbot - Nova on the App S X + K C O File | /Users/ashleyude/Downloads/MATH_1036_Assignment%201_2023SP_SPopichak%20(1).pdf A MATH_1036_Assignment 1_2023SP_SPopichak (1).pdf 11 / 11 | - 100% + 13. Evaluate: (a) d dx (23 + 9) 2 -2 8 9 ( b ) sec x dx 1 + tan x / x= 10 MATH 1036EL Page:11 11D2L Units - CHMI 2220EL 10-Clinic: x *Course Hero X MATH_1036_Assignment 1_20 x Al Chatbot - Nova on the App S X + K C O File | /Users/ashleyude/Downloads/MATH_1036_Assignment%201_2023SP_SPopichak%20(1).pdf A MATH_1036_Assignment 1_2023SP_SPopichak (1).pdf 10 / 11 | 100% + 12. Find the derivatives of the following functions: (a) y= z V/3x2 + 7 8 ( b) f (20 ) = 11- 221 9 10 (c) f(t) = tsint + costD2L Units - CHMI 2220EL 10-Clinic: x *Course Hero X MATH_1036_Assignment 1_20 x Al Chatbot - Nova on the App S X + K C O File | /Users/ashleyude/Downloads/MATH_1036_Assignment%201_2023SP_SPopichak%20(1).pdf #O A MATH_1036_Assignment 1_2023SP_SPopichak (1).pdf 9 / 11 | 100% + 11. (a) i. Draw a rough graph of y = 23 in the interval -2 5 x 5 2. 8 ii. Check that the point (2, 8) lies on your graph and find the tangent to y = x3 at 9 the point (2, 8). (b) Find all points on the curve y = 23 - x + 1 where the tangent line is parallel to the line y = 2x + 5. 10D2L Units - CHMI 2220EL 10-Clinic: X *Course Hero X MATH_1036_Assignment 1_20 x Al Chatbot - Nova on the App S X + K C O File | /Users/ashleyude/Downloads/MATH_1036_Assignment%201_2023SP_SPopichak%20(1).pdf A MATH_1036_Assignment 1_2023SP_SPopichak (1).pdf 8 / 11 | 100% + 10. Calculate the following derivatives (you may use appropriate rules and formulas in your calculation): dy (a) da where y = VI (+ 2 ) 8 a f (x) where f(z ) = azz + 6 cx2 + d and a, b, c, d are constants 9 10 MATH 1036EL Page:8 - + () .D2L Units - CHMI 2220EL 10-Clinic: X *Course Hero X MATH_1036_Assignment 1_20 x Al Chatbot - Nova on the App S X + K C O File | /Users/ashleyude/Downloads/MATH_1036_Assignment%201_2023SP_SPopichak%20(1).pdf A MATH_1036_Assignment 1_2023SP_SPopichak (1).pdf 7 / 11 | 100% + 7 MATH 1036EL Page:7 8 9. Calculate the derivatives of the following function directly from the definition of the deriva- tive (show steps): 1+x y = 2 - x 9D2L Units - CHMI 2220EL 10-Clinic: X *Course Hero X MATH_1036_Assignment 1_20 x Al Chatbot - Nova on the App S X + K C O File | /Users/ashleyude/Downloads/MATH_1036_Assignment%201_2023SP_SPopichak%20(1).pdf A MATH_1036_Assignment 1_2023SP_SPopichak (1).pdf 6 / 11 | 100% + 7. Calculate the following limits: (justify any cancelling) (a) lim 2 x-+ 1 72 - 1 6 (b) lim g(x), given that: 3 - x - x2