Ludium - Learn by Doing

Calculus 2

01The Four Properties of ln(x)02The Integral of 1/x 03Derivatives of ln(x)04Logarithmic Differentiation 05Integrating 1/u with the Natural Log 06Integrals of tan x and sec x Problem set0/10 Problem set 20/10 Practice∞

01Inverse Functions 02Evaluating f⁻¹(a) Without Finding f⁻¹(x)03Derivatives of Inverse Functions Problem set0/10 Problem set 20/10 Practice∞

01Defining e via the Integral of 1/t 02Solving Exponential & Logarithmic Equations 03Limits of e^x and ln(x)04Derivatives of e^x and the Chain Rule 05u-Substitution with Exponentials Problem set0/10 Problem set 20/10 Practice∞

01Derivatives of Exponential Functions 02Logarithmic Differentiation 03Integrating a^x and the Role of ln(a)04Derivatives of Logarithms with Any Base Problem set0/10 Problem set 20/10 Practice∞

01Inverse Trig Functions and Their Ranges 02Evaluating Inverse Trig Compositions 03Inverse Trig Derivatives 04Recognizing Inverse Trig Integral Forms 05u-Substitution with Leftover Variables Problem set0/10 Problem set 20/10 Practice∞

01Hyperbolic Functions 02Derivatives and Integrals of Hyperbolic Functions 03Inverse Hyperbolic Functions as Logarithms 04Derivatives of Inverse Hyperbolic Functions Problem set0/10 Problem set 20/10 Practice∞

01L'Hôpital's Rule 02Repeated L'Hôpital's Rule 03Indeterminate Forms ∞−∞ and 0·∞04Indeterminate Powers: 0⁰, ∞⁰, and 1^∞Problem set0/10 Problem set 20/10 Practice∞

01Integration by Parts 02Two Tricks for Integration by Parts 03Integrating Odd Powers of Secant 04Reduction Formula for ∫sinⁿ(x) dx Problem set0/10 Problem set 20/10 Practice∞

01Odd-Power Trig Integrals 02Half-Angle Identities for Even-Power Trig Integrals 03Integrals of tan^m·sec^n: A Two-Case Playbook 04Product-to-Sum Identities for Integration Problem set0/10 Problem set 20/10 Practice∞

01The Core Idea Behind Trig Substitution 02The Three Standard Trig Substitutions 03Trig Substitution: Sine and Tangent Cases 04Secant Substitution and the Hidden u-Sub 05Stacked Substitutions for Quadratic Radicals Problem set0/10 Problem set 20/10 Practice∞

01Partial Fractions: Distinct Linear Factors 02Long Division and the Cover-Up Method 03Partial Fractions with Repeated Linear Factors 04Irreducible Quadratics and Arctangent 05Repeated Irreducible Quadratics Problem set0/10 Problem set 20/10 Practice∞

01Improper Integrals on Infinite Intervals 02The p-Test for Improper Integrals 03Improper Integrals and Indeterminate Products 04Improper Integrals at Vertical Asymptotes 05Splitting Improper Integrals and Comparison Test Problem set0/10 Problem set 20/10 Practice∞

01General and Particular Solutions 02Separable Differential Equations 03Exponential Growth and Decay Models 04Newton's Law of Cooling Problem set0/10 Problem set 20/10 Practice∞

01Reading Sequence Notation and Finding Terms 02Finding the Formula of a Sequence 03Recursive Sequences 04Convergence and Divergence of Sequences 05Four Tools for Indeterminate Limits 06Proving a Sequence Is Monotonic 07The Monotone Convergence Theorem Problem set0/10 Problem set 20/10 Practice∞

01Convergence and the Sequence of Partial Sums 02Telescoping Series and Partial Fractions 03The Geometric Series 04Geometric Series: Convergence and Sums 05Divergence Test and the Harmonic Series 06Convergence of Split Series 07Finding the First Term in Geometric Series Problem set0/10 Problem set 20/10 Practice∞

01The Integral Test for Series 02Integral Test: Verifying the Decreasing Condition 03The p-Series Convergence Test 04The Integral Test: Conditions and U-Substitution Problem set0/10 Problem set 20/10 Practice∞

01The Comparison Test for Series 02The Direct Comparison Test 03The Comparison Test: Valid Cases and Limitations 04The Limit Comparison Test 05The Divergence Test and Series Convergence 06Applying the Limit Comparison Test by End Behavior Problem set0/10 Problem set 20/10 Practice∞

01Writing Alternating Series with the (-1) Factor 02Why the Alternating Series Test Works 03Applying the Alternating Series Test 04The Alternating Series Error Bound 05Approximating a Sum to a Set Accuracy Problem set0/10 Problem set 20/10 Practice∞