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We will discuss many of the basic manipulations of logarithms that commonly occur in Calculus (and higher) classes. Included is a discussion of the natural (ln(x) ln (x)) and common logarithm (log(x) log (x)) as well as the change of base formula.
Here is a set of practice problems to accompany the Functions Section of the Review chapter of the notes for Paul Dawkins Calculus I course at Lamar University.
Learn skills and concepts of calculus through questions and problems presented along with their detailed solutions.
Squeeze Theorem Examples. Use the squeeze theorem to prove the following important trigonometric limit. \lim_ {\theta\rightarrow 0} \frac {\sin (\theta)} {\theta} = 1 limθ→0 θsin(θ) = 1.
Math 1101 Calculus I Practice Midterm 1 Solutions 5. Compute the value of the derivative of f(x) at the point a. If f(x) is not di erentiable at a, explain why. (a) (3 points) f(x) = x3 + p x, a = 4 Solution: Write f(x) = x3 + x12 and using the power rule we see that f0(x) = 3x2 + 1 2 x(1 2 1) = 3x2 + 1 2 x 1 2 = 3x2 + 1 2 p x Plugging in a = 4 ...
Infinity. Is infinity at the end of the real number line? If F (x) is the antiderivative of f (x), is it true that. \int_a^b ∫ ab f (x)dx=F (b)-F (a)? Do local extrema occur if and only if f' (x) = 0? Is Infinity / Infinity = 1? Is infinity times zero = zero? What is 1 divided by 0? If the limit of a sequence is 0, does the series converge?
Compute the domain of a function: domain of f (x) = x/ (x^2-1) Compute the range of a function: range of e^ (-x^2) More examples. Calculus and analysis calculators and examples. Answers for integrals, derivatives, limits, sequences, sums, products, series expansions, vector analysis, integral transforms, domain and range, continuity.
Problems on integrating certain rational functions by partial fractions. Problems on power substitution. Problems on integration by trigonometric substitution. Problems on the area of an enclosed region in two-dimensional space. Problems on the volume of static solids by cross-sectional area.
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Calculus 2 6 units · 105 skills. Unit 1 Integrals review. Unit 2 Integration techniques. Unit 3 Differential equations. Unit 4 Applications of integrals. Unit 5 Parametric equations, polar coordinates, and vector-valued functions. Unit 6 Series. Course challenge. Test your knowledge of the skills in this course.