Mathematics Final Assessment 2021 Semester 1 Mathayom 6/1/2

Master Calculus! Practice derivatives & limits.

Type your name, student number and class below: This examination consists of 60 items = 30 points. Part 1. Multiple-Choice. Click the letter of the correct answer.1) Find the derivative of the following: f(x) = (5x + 3)4 . 20(3x + 5)3 20(x + 5)3 15(5x + 3)3 20(5x + 3)3 2) Find the derivative of the following: f(x) = (x2 - 3x)5 . (10x - 15)(x2 - 3x)4 (10x + 15)(x2 + 3x)4 (15x - 15)(x2 - 3x)4 (2x - 15)(x3 - 3x)4 3) Find the derivative of f(x) = sin(6x) . 7cos(6x) -6cos(6x) 6cos(6x) -7cos(-7x) 4) Find the derivative of f(x) = cos(x2) . -3xsin(x2) -2xsin(x2) -2xsin(x3) 3xsin(x2) 5) Find the derivative of f(x) = tan(x3) . 3x2 sec2(x3) 2x2 sec2(x2) x2 sec2(x3) x3 sec2(x3) 6) Find the derivative of f(x) = sec(4x) . sec(4x) tan(4x) 4sec(4x) tan(4x) -4sec(4x) tan(4x) 4xsec(4x) tan(4x) 7) Find the derivative of f(x) = sin(tan(x4)) . 4x2cos(tanx4) sec2(x4) -4x2cos(tanx4) sec2(x4) 4x3cos(tanx4) sec2(x4) x2cos(tanx4) sec2(x4) 8) Find the derivative of f(x) = cos2x.Note: sin 2x = 2 sin x . cos x sin(2x) cos(2x) -sin(2x) sin(x2) 9) Evaluate the following: 3x2 3x2 x2 x2 10) Evaluate the following: -x -2x 8x -6x 11) Find the derivative of f(x) = x3(4x + 5)4 . 3x2(4x + 5)4 + 16x3(4x + 5)3 x2(4x + 5)4 + 16x3(4x + 5)3 3x2(4x - 5)4 + 16x3(4x - 5)3 3x2(x + 5)4 + 16x4(4x + 5)2 12) Find the derivative of f(x) = 8sec x - 5cos x . 8csc x tan x + 5 sin x 8sec x tan x + 5 sin x 5csc x tan x + 8 sin x 8sec x tan x - 5 sin x 13) Find the derivative of f(x) = 2cot x - 7csc x . 2csc2x + 7csc x cot x -2csc2 x - 7csc x cot x -2csc2 x + 7csc x cot x 2csc2 x - 7csc x cot x 14) Find the derivative of f(x) = sec(7x) . 8csc (8x) tan (8x) -8csc (8x) tan (8x) 8sec2 (8x) tan (8x) 8sec (8x) tan (8x) 15) Find the derivative of f(x) = tan (x4) . 4x2sec2(x3) 4x3sec2(x4) -4x2sec2(x4) 2x3sec2(x4) 16) Find d [sin(7x)] . 7cos(8x) 7cos(7x) 14cos(7x) sin(7x) 17) Find d . -2sin(2x) 2sin(2x) sin(2x) 2cos(2x) 18) Find d (cot x) . csc2 x -cos x -csc2 x sec x tan x 19) Find d (5sec x + 2cos x) . 5 sec x tan x + 2 sin x sec x tan x - sin x sec x tan x + 2 sin x 5 sec x tan x - 2 sin x 20) Find d (cot x + 2csc x) . -csc2 x - 2csc x cot x csc2 x + 2csc x cot x csc2 x - csc x cot x -csc2 x + 2csc x cot x Part 2. Matching-Type. Drag to match. 1) d (sin x) cos x 2) d (cos x) -sin x 3) d (tan x) sec^2 x 4) d (csc x) -csc x cot x 5) d (sec x) sec x tan x Part 3. Find the limit of the following functions. If the limit does not exist, type dne. 13 13 13 37 47 dne 2 2 2 24 31 dne -2 4 dne -5 15 dne Part 4. Find the limit of the following functions at infinity. Type dne if the limit does not exist. 4 1 3 0 5 1 Part 5. Find the limit of the following trigonometric functions. 5 0 1 8 3 1 5 6 3 9 2