By Mark Zegarelli
An easy-to-understand primer on complicated calculus topics
Calculus II is a prerequisite for plenty of renowned university majors, together with pre-med, engineering, and physics. Calculus II For Dummies bargains professional guideline, recommendation, and the way to aid moment semester calculus scholars get a deal with at the topic and ace their exams.
It covers intermediate calculus themes in undeniable English, that includes in-depth assurance of integration, together with substitution, integration thoughts and whilst to take advantage of them, approximate integration, and mistaken integrals. This hands-on advisor additionally covers sequences and sequence, with introductions to multivariable calculus, differential equations, and numerical research. better of all, it comprises sensible workouts designed to simplify and improve knowing of this advanced subject.
creation to integration
Intermediate Integration topics
Confounded by means of curves? confused by way of polynomials? This plain-English advisor to Calculus II will set you straight!
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Additional info for Calculus II For Dummies (2nd Edition)
Figure 2-4: Graphs of three polynomial functions y = x 2, y = x 3, and y = x 4. 5 Exponential and logarithmic functions Here are some exponential functions with whole number bases: y = 2x y = 3x y = 10x Notice that for every positive base, the exponential function ✓ Crosses the y-axis at y = 1 ✓ Explodes to infinity as x increases (that is, it has an unbounded y value) ✓ Approaches y = 0 as x decreases (that is, in the negative direction the x-axis is an asymptote; you can read about these later) Chapter 2: Dispelling Ghosts from the Past: A Review of Pre-Calculus and Calculus I The most important exponential function is ex.
Y y = In x Figure 2-6: Graph of the logarithmic function y = ln x. 1 x Notice that this function is the reflection of ex along the diagonal line y = x. So the log function does the following: ✓ Crosses the x-axis at x = 1 ✓ Explodes to infinity as x increases (that is, it has an unbounded y value), though more slowly than any exponential function ✓ Produces a y value that approaches –∞ as x approaches 0 from the right 45 46 Part I: Introduction to Integration Furthermore, the domain of the log functions includes only positive values.
Polynomials enjoy a special status in math because they’re particularly easy to work with. For example, you can find the value of f(x) for any x value by plugging this value into the polynomial. Furthermore, polynomials are also easy to differentiate and integrate. Knowing how to recognize polynomials when you see them will make your life in any math course a whole lot easier. Powering through powers (exponents) Remember when you found out that any number (except 0) raised to the power of 0 equals 1?