Math 261, Calculus I, Calculus Stewart 8th edition. Topological definition of limit, epsilon and delta tolerance definition of limit, epsilon and delta definition of limit, proof of uniqueness of limit, proof that two sided limit exists if and only if both one sided limits exist and are equal, proof that if limit is positive then function is positive in some deleted neighborhood, proof that limit of constant is the constant, proof that as x approaches a then x approaches a, proof limit of linear function is the linear function evaluated at that point, proof of equivalent forms of a limit, proof limit of function is 0 if and only if the limit of its absolute value is 0, proof limit function existing implies limit of absolute value equals absolute value of its limit, counterexample showing limit of absolute value existing does not imply the limit with absolute value exists, proof that limit of sums is sum of limits, proof product of limits is limit of product, proof of limit of reciprocal is the reciprocal of its nonzero limit, proof of limit of quotient is quotient of limits if not dividing by 0, proof of limit of scalar multiple is scalar multiple of limit, proof that limit of difference is difference of limits, proof that limit of quotient does not exist if limit of numerator is not 0 and the limit of the denominator is 0, proof that limit of square is square of limit, proof that limit of cube is cube of limit, proof limit of power function with natural number exponent is power function of limit, use mathematical induction to show limit of function to a natural number exponent is that natural number exponent of the limit, use mathematical induction to show that the limit of a finite sum of functions is the sum of their limits, proof that limit of a polynomial is the polynomial at that limit, proof that limit of rational function is the rational function at that limit, proof of squeeze theorem, proofs for some infinite limits
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