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2.1 - A Preview of Calculus: #1-3, 7-12, 16-17, 22-25
Secant Lines and Tangent Lines: Check out the desmos graph here to get a visual of secant and tangent lines.
Approximation of the Area Under a Curve: Check out the desmos graph here to see the approximation of area under a curve using rectangles.
2.2 - The Limit of a Function: #30-31, 35-39, 44, 46-54, 59-64, 81, 82
2.3 - The Limit Laws: #83-97, 100-102, 104-114 evens, 115-117 all, 118-124 evens, 126-128, choose 129 or 130
2.4 - Continuity: #131-133, 138, 139, 142, 145, 146, 149-152, 154, 156, 162-167, 170-172
Hint for #170-172: Recall from physics that F = ma, where m is the mass of the object, and a is acceleration due to gravity. Watch our for unit differences and convert appropriately!
2.5 - The Precise Definition of the Limit: (no homework)
Below are a couple of desmos graphs showing how this idea works in general for a couple of key functions.
3.1 - Defining the Derivative: #2, 4, 6, 8, 9, 12, 15, 17, 18, 26, 29, 30, 35, 36, 38-41, 43, 47, 51
3.2 - The Derivative as a Function: #54, 56, 57, 59, 62, 64-75, 77-82, 90, 93, 95, 97-99
Below is a desmos graph showing the relationship between the output of the derivative function and the slope of the tangent line.
3.3 - Differentiation Rules
3.3A: #106-109, 118, 122, 130, 133, 135, 137, 140, 142-144
3.3B: #110, 112, 113, 116, 117, 119, 120, 123-126, 128, 131, 132, 134, 136, 138, 139, 141
3.4 - Derivatives as Rates of Change: #150-154, 156, 157, 159, 160, 162, 165
3.5 - Derivatives of Trigonometric Functions: #176, 180, 184, 192, 198, 200, 204, 210
3.6 - The Chain Rule: #214, 215, 220, 223, 229, 231, 238-240, 242, 243, 245-248, 251, 253
3.7 - Derivatives of Inverse Functions: #260-265, 268-271, 273-275, 277, 280, 283, 289-292, 296, 298
For number 273, use domain restriction on interval [-0.1, pi/2)
3.8 - Implicit Differentiation: #300-305, 308, 310, 312, 314, 316, 318, 320, 324-327
A desmos graph with examples of implicitly differentiated equations can be found below.
3.9 - Derivatives of Exponential and Logarithmic Functions: #332, 336, 338, 342, 347, 351, 354, 358, 362
4.1 - Related Rates: #2, 4, 7, 10, 14, 15, 18, 20, 24, 25, 30, 42, 45
4.2 - Linear Approximation and Differentials: #48, 49, 52, 54, 76, 80, 82, 84, 86
4.3 - Maxima and Minima: #92, 98, 102, 106, 110, 112, 116, 120, 124, 125, 127, 134, 136, 142-144
4.4 - The Mean Value Theorem: #148-156 (evens), 162-174 (evens), 180, 190, 192
4.5 - Derivatives and the Shape of a Graph: #195, 196, 198, 200, 206, 208, 214-220 (evens), 226, 228, 232, 238, 246-250 (evens)
4.6 - Limits at Infinity and Asymptotes: #256, 258, 264, 266, 270, 276, 278, 282, 308, 310 *Note: Whenever possible, all questions should be answered using limits...
4.7 - Applied Optimization Problems: #312-315, 320, 322, 323 (it's the Moving Sofa Problem!), 330-332 (try doing 334 first to get an idea of how to attack 332), 338, 344, 350, 354
4.8 - L'Hospital's Rule: #356, 358, 362, 364, 368, 372, 376, 388, 390, 394
4.9 - Newton's Method: #407, 409, 415, 421, 425, 431, 441, 443, 461
4.10 - Antiderivatives: #467, 471, 473, 475, 481, 489, 493, 495, 499, 503, 507, 511, 521, 522
5.1 - Approximating Areas: #1, 9, 13, 17, 21, 23, 27, 35, 37, 43, 45
5.2 - The Definite Integral: #61, 65, 69, 71, 75, 79, 81, 85, 89, 93, 95 (Revised 2/26/25: 101, 105, 115, 127, 141)
5.3 - The Fundamental Theorem of Calculus: #145, 147, 149, 151, 153, 158, 159, 163, 167, 173, 181, 185, 189, 193, 195, 202, 205 (Sorry! That's a long one...but it's so important!)
5.4 - Integration Formulas and the Net Change Theorem: #207-215 odds, 221, 223, 229, 239
5.5 - Substitution: #255, 259, 261, 265, 269, 271, 277, 279, 283, 287, 293, 297, 311, 317
5.6 - Integrals Involving Exponential and Logarithmic Functions: #321, 325, 327, 329, 333, 335, 339, 341, 343 (use a twist on the hint on 342), 347, 353, 359, 363, 377, 388 *attempt*
5.7 - Integrals Resulting in Inverse Trigonometric Functions: #391, 393, 397, 399, 401, 403, 411, 413, 425, 431, 435
6.1 - Areas Between Curves: #1-6, 7-13 (odds), 21, 25, 37, 43[ T ], 45[ T ], 47[ T ], 51
6.2 - Determining Areas by Slicing: #63, 67, 69, 71, 73, 75, 79, 80, 83, 89, 93, 101, 105-107
Complete the following problems as one assignment
4.1 - Basics of Differential Equations: #15, 17, 19, 25, 33, 41
4.2 - Direction Fields and Numerical Methods: #70-72, 77, 83, 84-88
4.3 - Separable Equations: #119, 121, 125, 129, 131, 133, 149, 157, 167