Calculus I

Course Description

In this course, Krista King from the integralCALC Academy covers a range of topics in Calculus I, including Precalculus, Limits & Continuity, Derivatives and Applications of Derivatives.

Calculus I
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Video Lectures & Study Materials

Visit the official course website for more study materials:

# Lecture Play Lecture
1 Vertical Line Test Overview (003:49) Play Video
2 Domain and Range (002:57) Play Video
3 Finding Values and Domain and Range from a Graph (004:44) Play Video
4 Equation Modeling (006:46) Play Video
5 Modeling the Equation of a Piecewise Defined Function from its Graph (005:46) Play Video
6 Sketching a Graph from a Story Problem (004:25) Play Video
7 Determining if a Function is Even, Odd or Neither (004:23) Play Video
8 How to Classify Functions (005:23) Play Video
9 Equation of the Line in Slope-intercept Form (006:50) Play Video
10 Equation of a Line in Point-slope Form (008:50) Play Video
11 Least Squares Line (007:50) Play Video
12 Finding the Inverse of a Function (002:27) Play Video
13 Sketch the Graph of a Parabola (009:46) Play Video
14 Finding the Center and Radius of the Circle (004:57) Play Video
15 Sketch the Graph of a Circle (007:13) Play Video
16 Combinations of Functions and their Domains (006:18) Play Video
17 Composite Functions (002:40) Play Video
18 Composite Functions and their Domains (0013:59) Play Video
19 Describing Transformations Algebraically (005:30) Play Video
20 Graphing Transformations (006:23) Play Video
21 Using Transformations to Sketch a Graph (004:46) Play Video
22 Determine Whether a Function is 1 to 1 (004:26) Play Video
23 Find the Inverse of a Function and Sketch its Graph (005:22) Play Video
24 Finding the Linear Function Given Two Points on its Inverse (006:27) Play Video
25 Use Laws of Logarithms to Simplify a Logarithmic Function (004:35) Play Video
26 Use the Quadratic Formula to Find Roots of the Function (004:51) Play Video
27 Completing the Square of a Quadratic Function (005:26) Play Video
28 Polynomial Long Division for Rational Functions (005:15) Play Video
29 Hyperbolic Identities (005:18) Play Video
30 Limits: Substitution Method (001:43) Play Video
31 Limits: Factoring Method (002:14) Play Video
32 Limits: Conjugate Method (004:19) Play Video
33 Use Limit Laws to Evaluate Limits of Combination Functions (009:28) Play Video
34 Limits: Crazy Graphs (006:56) Play Video
35 Limits at Infinity (009:56) Play Video
36 Infinite Limits (007:40) Play Video
37 Limits: Trigonometric (Example 2) (004:40) Play Video
38 Limits: One-Sided (006:53) Play Video
39 How to Prove that the Limit Does Not Exist (006:07) Play Video
40 Precise Definition of the Limit (009:28) Play Video
41 Finding Delta from a Graph and the Epsilon-delta Definition of the Limit (006:45) Play Video
42 Squeeze Theorem (004:33) Play Video
43 Limit of an Inequality with Squeeze Theorem (003:31) Play Video
44 Continuity (003:32) Play Video
45 Removable Discontinuity (007:06) Play Video
46 Finding the Value that Makes the Function Continuous (003:17) Play Video
47 Intermediate Value Theorem Overview (004:09) Play Video
48 Intermediate Value Theorem to Prove a Root in an Interval (004:57) Play Video
49 Prove the Equation Has at Least One Real Root (006:59) Play Video
50 How to Calculate the Difference Quotient (004:11) Play Video
51 Power Rule (005:27) Play Video
52 Derivatives of Linear Combinations (004:40) Play Video
53 Product Rule (0010:32) Play Video
54 Product Rule - 3+ Functions (007:26) Play Video
55 Quotient Rule (0012:31) Play Video
56 Reciprocal Rule (008:52) Play Video
57 Chain Rule (004:10) Play Video
58 Chain Rule for Derivatives with Product Rule (009:14) Play Video
59 Chain Rule for Derivatives with Quotient Rule (007:54) Play Video
60 Chain Rule for Derivatives with Trig Functions (005:42) Play Video
61 Trigonometric Derivatives: Overview (0014:59) Play Video
62 Trigonometric Derivatives (Example 1) (006:55) Play Video
63 Derivatives of Inverse Trig Functions: arcsin (005:09) Play Video
64 Derivatives of Inverse Trig Functions: arccot (004:27) Play Video
65 Derivatives of Hyperbolic Functions (002:55) Play Video
66 Derivative of an Inverse Hyperbolic Function (005:14) Play Video
67 Derivatives of Natural Logs (ln) (0011:46) Play Video
68 Use Laws of Logarithms to Find the Derivative (006:16) Play Video
69 Derivatives of Exponentials (e^x) (005:40) Play Video
70 Equation of the Tangent Line (0017:05) Play Video
71 Differentiability and Vertical Tangent Lines (0011:55) Play Video
72 Equation of the Normal Line at a Point (005:07) Play Video
73 Average Rate of Change (004:29) Play Video
74 Implicit Differentiation (0010:19) Play Video
75 Use Implicit Differentiation to Find the Equation of the Tangent Line at a Point (0012:53) Play Video
76 Use Implicit Differentiation to Find the Second Derivative of y (y'') (008:49) Play Video
77 Half Life (006:13) Play Video
78 Continuously Compounded Interest (002:36) Play Video
79 Sales Decline (006:01) Play Video
80 Linear Approximation in One Variable (005:38) Play Video
81 Linearization of a Function at a Point (004:15) Play Video
82 Critical Points (009:53) Play Video
83 Increasing and Decreasing (Example 1) (005:22) Play Video
84 Concavity and Inflection Points (006:37) Play Video
85 First Derivative Test (0012:59) Play Video
86 Second Derivative Test: One Variable (005:00) Play Video
87 Vertical Asymptotes: Overview (0011:20) Play Video
88 Horizontal Asymptotes: Basic Overview (004:46) Play Video
89 Horizontal Asymptotes: Further Detail (0011:08) Play Video
90 Slant Asymptotes (004:07) Play Video
91 Sketching Graphs (Example 1) (007:38) Play Video
92 Maxima and Minima on a Closed Range (0015:52) Play Video
93 Dimensions that Minimize the Surface Area of a Cylinder (008:58) Play Video
94 Largest Area of a Rectangle Inscribed in a Semicircle (0016:09) Play Video
95 Dimensions that Maximize the Area of the Rectangle (006:28) Play Video
96 Largest Possible Volume of a Cylinder Inscribed in a Sphere (0014:26) Play Video
97 Maximum Volume of a Cone Shaped Cup (0011:27) Play Video
98 Dimensions of the Rectangle with Largest Area Inscribed in an Equilateral Triangle (0013:39) Play Video
99 Applied Optimization: Two Real Numbers with Difference 20 and Minimum Possible Product (0010:13) Play Video
100 Applied Optimization: Area and Margins of a Page (0014:28) Play Video
101 Related Rates: Radius of a Balloon and Changing Price (0012:37) Play Video
102 Related Rates: Water Level in a Tank (008:28) Play Video
103 Related Rates: Ladder Sliding Down a Wall (008:44) Play Video
104 Related Rates: Distance Between Observer and Airplane (009:07) Play Video
105 Mean Value Theorem (008:30) Play Video
106 Rolle's Theorem (007:02) Play Video
107 Newton's Method (008:09) Play Video
108 L'Hopital's Rule (005:25) Play Video
109 Position Function (003:08) Play Video
110 All About a Particle's Position Function (0019:51) Play Video
111 Vertical Motion (Differentiation) (0011:47) Play Video
112 Marginal Cost, Revenue and Profit (004:53) Play Video


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