Limits

Formulas are organized based on their importance in the CAT exam.
1 Logarithmic Limit
2 Related Rates
3 Continuity Does Not Imply Differentiability
4 Standard Trigonometric Limit 2
5 Standard Sine Limit with Two Functions
6 Monotonicity from the Derivative
7 Limit of a Constant
8 Limit of a Polynomial
9 Non-Decreasing Function
10 Concave Upward
11 Second Derivative Test for Local Maximum
12 First Derivative Test for Local Minimum
13 Continuity of Rational Functions
14 Evaluation of the Form $$\infty^0$$
15 Angle Between Two Curves
16 Sandwich Theorem
17 Derivative of a Constant Multiple
18 Standard Algebraic Limit
19 Standard Limit with a Polynomial Argument
20 Infinite Limit
21 Derivative of Inverse Cosine
22 Exponential Limit 2
23 Limit of a Function
24 Limit of a Rational Function
25 Derivative of Inverse Cosecant
26 Basic Limit Properties
27 Limit at Infinity
28 Reciprocal Tangent Limit
29 Standard Limit Involving Cosine
30 Difference of Powers
31 Derivative of a Function of a Function
32 Standard Limit Involving Sine
33 Equivalent Cosine Form
34 Standard Exponential Limit
35 Generalized Tangent Limit
36 Reciprocal Exponential Limit
37 Standard Trigonometric Limit 1
38 Reciprocal Logarithmic Limit
39 Reciprocal Sine Limit
40 Standard Logarithmic Limit
41 Derivative of a General Power Function
42 Exponential Limit 1
43 Important Equivalent Infinitesimals
44 Limit of a Power Function
45 Algebra of Continuous Functions
46 Local Maximum
47 Standard Limit Involving Tangent
48 Derivative of Inverse Secant
49 Product Rule
50 Evaluation of the Form $$0^0$$
51 First Derivative Test for Decreasing Function
52 Important Indeterminate Forms
53 Right-Hand Limit
54 Factorisation Method
55 Cauchy's Mean Value Theorem
56 Basic Trigonometric Identity for Limit Evaluation
57 Derivative of a Modulus of a Function
58 Chain Rule
59 Geometrical Form of LMVT
60 Difference Rule
61 L'Hôpital's Rule
62 Differentiability Implies Continuity
63 Fundamental Trigonometric Inequality
64 Rationalisation Method
65 Rational Function Limit at Infinity
66 Limit of a Continuous Elementary Function
67 Derivative of Sine Function
68 Conditions for Rolle's Theorem
69 Point of Inflection
70 Limit Laws
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