Calculus 1 Made Easy

Explain how to evaluate limits involving absolute value by analyzing the inner sign, using left and right limits, and the piecewise definition, with |x-2|/(x-2) yielding -1 as x approaches 2.

Solve a variety of calculus quiz questions on limits, left and right limits, and two-sided limits. Analyze the absolute value, piecewise functions, and the greatest integer function to assess continuity.

Master a quick trig limit shortcut: replace sin x and tan x with x as x approaches zero to simplify limits. Note exceptional additions or subtractions require other methods.

Evaluate limits at infinity by focusing on dominant terms and using two methods: multiply brackets to obtain the leading term, or keep highest degree terms in each bracket.

Master limit problems by analyzing left and right limits, identifying infinite behavior, and applying dominant-term techniques—divide by the highest degree to evaluate rational functions as x grows.

Learn to solve limits by identifying dominant terms, dividing by the highest degree, and using absolute values for square roots as x tends to infinity or negative infinity.

examine limits at infinity of sign x, sine x, and cosine x as x approaches infinity or negative infinity; they do not exist due to oscillation between -1 and 1.

Explore derivatives through power rule, product rule, and rewriting functions with negative exponents; apply them to evaluate derivatives at key values like -1, π, and 1.