Limits and Derivatives
Standard Algebraic Limit
Evaluates the indeterminate 0/0 limit of an algebraic power difference as x approaches a.
Standard Limit of sin x / x
Evaluates the fundamental trigonometric limit as x approaches 0 with angle in radians.
Standard Limit of tan x / x
Evaluates the standard limit for the tangent function as x approaches 0 in radians.
Standard Exponential Limit
Evaluates standard indeterminate limits involving exponential functions as exponent tends to 0.
Standard Logarithmic Limit
Evaluates the standard 0/0 limit of the natural logarithm as argument approaches 1.
Limit of Form 1 to Infinity
Evaluates limits having the indeterminate form 1^\infty when f(x) -> 1 and g(x) -> \infty.
L'Hopital's Rule
Evaluates limits of indeterminate forms 0/0 or \infty/\infty by differentiating numerator and denominator.
Maclaurin Series of e^x
Gives the power series expansion of the exponential function used to evaluate limits.
Maclaurin Series of ln(1+x)
Gives the logarithmic series expansion valid for -1 < x <= 1 used in limit evaluation.
Maclaurin Series of cos x
Gives the series expansion of cosine about x = 0 used to evaluate higher-order limits.
Definition of Derivative (First Principle)
Defines the instantaneous rate of change of f(x) from first principles.
Power Rule of Differentiation
Gives the derivative of x^n with respect to x for any real exponent n.
Product Rule of Differentiation
Gives the derivative of the product of two differentiable functions.
Quotient Rule of Differentiation
Gives the derivative of the quotient of two functions when the denominator is non-zero.
Derivatives of Trigonometric Functions
Gives standard derivatives of the fundamental trigonometric functions.