We will give the Fundamental Theorem of Calculus showing the relationship between derivatives and integrals.
This is often one of the more difficult sections for students. Limits - In this chapter we introduce the concept of limits. Solving Trig Equations with Calculators, Part I — In this section we will discuss solving trig equations when the answer will generally require the use of a calculator i.
Implicit Differentiation — In this section we will discuss implicit differentiation. This section is devoted to simply defining what an indefinite integral is and to give many of the properties of the indefinite integral. Stop struggling and start learning today with thousands of free resources!
If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width. Computing Limits — In this section we will looks at several types of limits that require some work before we can use the limit properties to compute them.
We will discuss many of the basic manipulations of logarithms that commonly occur in Calculus and higher classes. We will give an application of differentials in this section. Wyzant Resources features blogs, videos, lessons, and more about Math and over other subjects.
Integral Calculus Integral calculus involves the concept of integration. One-Sided Limits — In this section we will introduce the concept of one-sided limits.
We can use the lienar approximation to a function to approximate values of the function at certain points. Computation and Properties of the Derivative in Calculus.
Exponential and Logarithm Equations — In this section we will discuss various methods for solving equations that involve exponential functions or logarithm functions. Still need help after using our calculus resources? Continuity — In this section we will introduce the concept of continuity and how it relates to limits.
More importantly, however, is the fact that logarithm differentiation allows us to differentiate functions that are in the form of one function raised to another function, i.
Here is a listing of sections for which practice problems have been written as well as a brief description of the material covered in the notes for that particular section. A set of questions on the concepts of a function, in calculus, are presented along with their answers and solutions. We will also cover evaluation of trig functions as well as the unit circle one of the most important ideas from a trig class!
The examples in this section can all be done with a basic knowledge of indefinite integrals and will not require the use of the substitution rule. The integrals in this section will all require some manipulation of the function prior to integrating unlike most of the integrals from the previous section where all we really needed were the basic integration formulas.
We will discuss the Product Rule and the Quotient Rule allowing us to differentiate functions that, up to this point, we were unable to differentiate.
Definition of the Definite Integral — In this section we will formally define the definite integral, give many of its properties and discuss a couple of interpretations of the definite integral.
We will also discuss the process for finding an inverse function.
Note however, the process used here is identical to that for when the answer is one of the standard angles. Linear Approximations — In this section we discuss using the derivative to compute a linear approximation to a function.
Knowing implicit differentiation will allow us to do one of the more important applications of derivatives, Related Rates the next section.
More Substitution Rule — In this section we will continue to look at the substitution rule. Finding Absolute Extrema — In this section we discuss how to find the absolute or global minimum and maximum values of a function.
While it might not seem like a useful thing to do with when we have the function there really are reasons that one might want to do this. The topics are arranged in a natural progression catering typically to late highschool and early college students, covering the foundations of calculus, limits, derivatives, integrals, and vectors.
As we will see starting in the next section many integrals do require some manipulation of the function before we can actually do the integral. We will be estimating the value of limits in this section to help us understand what they tell us.
Trig Functions — In this section we will give a quick review of trig functions. Calculus I Here are a set of practice problems for the Calculus I notes.Calculus Questions with Answers (1). The uses of the first and second derivative to determine the intervals of increase and decrease of a function, the maximum and minimum points, the interval(s) of concavity and points of inflections are discussed.
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Calculus II Practice Problems 1: Answers 1. Solve for x: a) 6x x Answer.
Since 36 62, the equation becomes 6x 62 2 x, so we must have x 2 2 x which has the solution x 4 3. b) ln3 x 5 Answer. If we exponentiate both sides we get x 35 c) ln2 x 1 ln2 x 1 ln2 8 Answer.
Since the difference of logarithms is the logarithm of the quotient, we. A Collection of Problems in Di erential Calculus Problems Given At the Math - Calculus I and Math - Calculus I With Review Final Examinations Department of Mathematics, Simon Fraser University 5 True Or False and Multiple Choice Problems 81 6 Answers, Hints, Solutions Beginning Differential Calculus: Problems on the limit of a function as x approaches a fixed constant ; limit of a function as x approaches plus or minus infinity ; limit of a function using the precise epsilon/delta definition of limit ; limit of a function using l'Hopital's rule.