Limits

Formulas are organized based on their importance in the CAT exam.
1 Non-Decreasing Function
2 First Derivative Test for Local Minimum
3 Second Derivative Test for Local Maximum
4 Related Rates
5 Evaluation of the Form $$\infty^0$$
6 Concave Upward
7 Derivative of a Constant Multiple
8 Derivative of Inverse Cosine
9 Angle Between Two Curves
10 Continuity of Rational Functions
11 Standard Trigonometric Limit 2
12 Sandwich Theorem
13 Logarithmic Limit
14 Basic Limit Properties
15 Limit of a Function
16 Infinite Limit
17 Limit of a Rational Function
18 Limit of a Constant
19 Exponential Limit 2
20 Limit at Infinity
21 Derivative of Inverse Cosecant
22 Difference of Powers
23 Limit of a Polynomial
24 Standard Limit with a Polynomial Argument
25 Standard Algebraic Limit
26 Derivative of a Function of a Function
27 Standard Limit Involving Tangent
28 Reciprocal Tangent Limit
29 Standard Limit Involving Cosine
30 Equivalent Cosine Form
31 Standard Exponential Limit
32 Standard Trigonometric Limit 1
33 Standard Limit Involving Sine
34 Reciprocal Sine Limit
35 Generalized Tangent Limit
36 Reciprocal Exponential Limit
37 Reciprocal Logarithmic Limit
38 Standard Logarithmic Limit
39 Derivative of a General Power Function
40 Exponential Limit 1
41 Important Equivalent Infinitesimals
42 Standard Sine Limit with Two Functions
43 Limit of a Power Function
44 Derivative of a Modulus of a Function
45 Derivative of Inverse Secant
46 Algebra of Continuous Functions
47 Local Maximum
48 First Derivative Test for Decreasing Function
49 Important Indeterminate Forms
50 Product Rule
51 Chain Rule
52 Right-Hand Limit
53 Cauchy's Mean Value Theorem
54 Evaluation of the Form $$0^0$$
55 Basic Trigonometric Identity for Limit Evaluation
56 Factorisation Method
57 Geometrical Form of LMVT
58 Difference Rule
59 L'Hôpital's Rule
60 Differentiability Implies Continuity
61 Fundamental Trigonometric Inequality
62 Rationalisation Method
63 Rational Function Limit at Infinity
64 Limit of a Continuous Elementary Function
65 Derivative of Sine Function
66 Conditions for Rolle's Theorem
67 Point of Inflection
68 Limit Laws
69 Continuity Does Not Imply Differentiability
70 Monotonicity from the Derivative
71 Continuity Definition
72 Derivative of Absolute Value Function
73 Second Derivative Test Failure
74 Derivative from First Principle
75 Definition of Limit
76 Generalized Cosine Limit
77 Absolute Extrema on a Closed Interval
78 Squeeze Theorem
79 Orthogonal Curves
80 Continuity Condition Using One-Sided Limits
81 Darboux's Theorem
82 General Exponential Limit
83 Derivative of Exponential Function
84 Derivative as a Limit
85 Local Minimum
86 Logarithmic Differentiation
87 Parametric Differentiation
88 Limit Involving Inverse Tangent
89 Limits of Composite Functions
90 Generalized Sine Limit
91 Absolute Maximum
92 Sequence Limit Form
93 Limit Under a Continuous Function
94 Candidates for Absolute Extrema
95 Radical Limit Form
96 Necessary Condition for an Interior Extremum
97 General Tangent Ratio
98 Sine-Tangent Ratio
99 Exponential Ratio
100 Derivative of Composite Logarithm
101 Left-Hand Limit
102 Derivative of Cosine Function
103 General Logarithmic Limit
104 Derivative of Tangent Function
105 Derivative of Secant Function
106 Tangent to a Curve
107 Important Limit Involving $$\sin x$$
108 Derivative of Inverse Cotangent
109 Double-Angle Transformation
110 Composite Inverse-Trigonometric Derivative
111 Continuity on an Interval
112 Continuity of Polynomial Functions
113 Differentiability at a Point
114 Left-Hand Derivative
115 Decreasing Function
116 General Inverse-Tangent Limit
117 Derivative of the Inverse Function
118 Derivative of a Composite Power
119 Derivative of a Constant
120 Power Rule
121 General Sine Ratio
122 Derivative of a Composite Exponential
123 Sum Rule
124 Concave Downward
125 Exponential Representation of a Power
126 Derivative of Cosecant Function
127 Derivative of Composite Trigonometric Functions
128 Absolute Minimum
129 Standard Power-Exponential Limit
130 Evaluation of the Form $$1^\infty$$
131 Continuity of Composite Functions
132 Non-Increasing Function
133 First Derivative Test for Local Maximum
134 Derivative with Respect to Another Variable
135 Tangent Parallel to the y-Axis
136 Rate of Change
137 Derivative of a Polynomial
138 Differentiability of a Modulus Function at a Zero
139 Second Derivative Test for Local Minimum
140 Higher Derivative Test
141 General Binomial Limit
142 Implicit Differentiation
143 Logarithmic Method for Variable Powers
144 Derivative of Inverse Tangent
145 Derivative of Cotangent Function
146 Normal to a Curve
147 Tangent Parallel to the x-Axis
148 Continuity of a Modulus Function
149 Change of Variable in Limits
150 Critical Point
151 Second Derivative for Parametric Equations
152 Higher-Order Derivative
153 Lagrange Mean Value Theorem
154 Existence of a Two-Sided Limit
155 Continuity at a Point
156 Half-Angle Transformation
157 Constant Multiple Rule
158 Rolle's Theorem
159 Derivative of Inverse Sine
160 Derivative of a Product of Three Functions
161 Derivative of General Exponential Function
162 Increasing Function
163 Right-Hand Derivative
164 Logarithmic Ratio
165 Condition for Differentiability
166 Important Limit Involving $$\tan x$$
167 Quotient Rule
168 Derivative of Logarithm to Any Base
169 Indeterminate Forms
170 First Derivative Test for Increasing Function
171 Derivative of Natural Logarithm
172 Limit Involving Inverse Sine
173 Important Limit Involving $$1-\cos x$$
174 General Inverse-Sine Limit