Step by Step Calculus 1 : Learn from scratch

Explore limits and velocity concepts by analyzing a car's motion: from a function of time to average velocity to instantaneous velocity via the limit of time intervals.

Explore the three types of continuity—including removable and infinite discontinuities—through piecewise functions, limit analysis, and visual methods, with Gaussian and 1/x examples.

Explore lines and slopes, learn the line equation y = mx + b, and identify x-intercepts and y-intercepts while understanding slope as rise over run and its link to derivatives.

Explore the derivative at a point by constructing tangent lines that touch the curve at a single point, and use secant slopes and limits to find the tangent slope.

Learn step-by-step how to differentiate quotients using the quotient rule, with f(x)=x^2 and g(x)=x^3−2, deriving (f/g)' = (f' g − f g')/g^2 and applying it to an example.

practice problem demonstrates applying the quotient rule to differentiate f(x)/g(x) with g(x) = 5 sqrt(x) and f(x) involving a square root.

Apply the chain rule to differentiate a composite function with the outer tangent and inner three times the square root of x, multiplying derivatives.

Explores locating inflection points via the second derivative, deriving f''(x)=6x to find x=0 and the inflection point at (0,0), and examines how tangent slopes change across it.

Practice problem sketches the graph of x^3-4x by locating intersection points. It identifies maxima, minima, and inflection points and describes convex and concave regions before sketching.