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- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(Tradler_and_Carley)/23%3A_Sequences_and_Series/23.03%3A_ExercisesIn the case that it is part of an arithmetic sequence, find the formula for the \(n\)th term \(a_n\) in the form \(a_n=a_1+d\cdot (n-1)\). Find the sum of the first \(100\) terms of the arithmetic seq...In the case that it is part of an arithmetic sequence, find the formula for the \(n\)th term \(a_n\) in the form \(a_n=a_1+d\cdot (n-1)\). Find the sum of the first \(100\) terms of the arithmetic sequence: \(2, 4, 6, 8, 10, 12, \dots\) Find the sum of the first \(83\) terms of the arithmetic sequence: \(25, 21, 17, 13, 9, 5, \dots\) Find the sum of the first \(75\) terms of the arithmetic sequence: \(2012, 2002, 1992, 1982, \dots\)
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(Tradler_and_Carley)These are notes for a course in precalculus, as it is taught at New York City College of Technology - CUNY. Our approach is calculator based. For this, we will use the currently standard TI-84 calcula...These are notes for a course in precalculus, as it is taught at New York City College of Technology - CUNY. Our approach is calculator based. For this, we will use the currently standard TI-84 calculator, and many of the examples will be explained and solved with it. However, we want to point out that there are also many other calculators that are suitable for the purpose of this course and many of these alternatives have similar functionalities as the calculator that we have chosen to use.
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(Tradler_and_Carley)/09%3A_Graphing_Polynomials/9.03%3A_Optional_Section-_Graphing_Polynomials_by_HandNote, that on the calculator it is impossible to get a window which will give all of the features of the graph (while focusing on getting the maximum in view the other features become invisible). This...Note, that on the calculator it is impossible to get a window which will give all of the features of the graph (while focusing on getting the maximum in view the other features become invisible). This is the leading term of the polynomial (if you expand \(p\) it is the term with the largest power) and therefore dominates the polynomial for large \(|x|\). We pass through the point \((8,0)\) like a line and we join (perhaps with the use of an eraser) to the large \(x\) part of the graph.
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(Tradler_and_Carley)/19%3A_Inverse_Trigonometric_Functions
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(Tradler_and_Carley)/20%3A_Trigonometric_Equations/20.02%3A_Equations_involving_trigonometric_functionsx \approx 1.788+n \pi \quad \text { or } \quad x \approx 2.224+n \pi \quad \text { or } \quad x \approx 3.842+n \pi \quad \text { where } n=0, \pm 1, \pm 2, \pm 3, \ldots \end{aligned} \nonumber \]
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(Tradler_and_Carley)/27%3A_Reviews/27.03%3A_Review_of_exponential_and_logarithmic_functionsThe population of a country grows exponentially at a rate of \(1\%\) per year. If the population was \(35.7\) million in the year \(2010\), then what is the population size of this country in the year...The population of a country grows exponentially at a rate of \(1\%\) per year. If the population was \(35.7\) million in the year \(2010\), then what is the population size of this country in the year \(2015\)? How long do you have to wait until the substance has decayed to \(\dfrac 1 4\) of its original size? Assuming that \(x,y>0\), write the following expressions in terms of \(u=\log(x)\) and \(v=\log(y)\): Find the exact solution of the equation: \(6^{x+2}=7^x\)
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(Tradler_and_Carley)/26%3A_Appendix_A_-_Introduction_to_the_TI-84/26.09%3A_A.9-_Common_errorsThe calculator graphic is not really the graph, but has extra parts or missing parts of the graph (depending on the version of the calculator: TI-83 is much worse than TI-84). The reason for this is t...The calculator graphic is not really the graph, but has extra parts or missing parts of the graph (depending on the version of the calculator: TI-83 is much worse than TI-84). The reason for this is that the calculator just approximates the graph pixel by pixel and does not represent the exact graph. In particular, you should not just copy the graph from the calculator onto your paper, but interpret what you see and draw the interpreted graph!
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(Tradler_and_Carley)/21%3A_Complex_Numbers/21.03%3A_Exercises\(7\left(\cos\left(\dfrac{2\pi}{9}\right)+i\sin\left(\dfrac{2\pi}{9}\right)\right) \cdot 6\left(\cos\left(\dfrac{\pi}{9}\right)+i\sin\left(\dfrac{\pi}{9}\right)\right)\) \(\left(\cos\left(\dfrac{13\pi...\(7\left(\cos\left(\dfrac{2\pi}{9}\right)+i\sin\left(\dfrac{2\pi}{9}\right)\right) \cdot 6\left(\cos\left(\dfrac{\pi}{9}\right)+i\sin\left(\dfrac{\pi}{9}\right)\right)\) \(\left(\cos\left(\dfrac{13\pi}{12}\right)+i\sin\left(\dfrac{13\pi}{12}\right)\right) \cdot \left(\cos\left(\dfrac{-11\pi}{12}\right)+i\sin\left(\dfrac{-11\pi}{12}\right)\right)\) \(42\left(\cos \left(\dfrac{\pi}{3}\right)+i \sin \left(\dfrac{\pi}{3}\right) \right)=21+21 \sqrt{3} i\)
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(Tradler_and_Carley)/16%3A_Half-life_and_Compound_Interest/16.02%3A_Compound_InterestThe reason the exponential function appears in the above formula is that the exponential is the limit of the previous formula in observation \(n\)th-compounding, when \(n\) approaches infinity; compar...The reason the exponential function appears in the above formula is that the exponential is the limit of the previous formula in observation \(n\)th-compounding, when \(n\) approaches infinity; compare this with equation 13.1.1. Find the amount \(P\) that needs to be invested at \(4.275 \%\) compounded annually for \(5\) years to give a final amount of \(\$ 3000\). (This amount \(P\) is also called the present value of the future amount of \(\$3000\) in \(5\) years.)
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(Tradler_and_Carley)/04%3A_Introduction_to_the_TI-84
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(Tradler_and_Carley)/05%3A_Basic_Functions_and_Transformations/5.03%3A_ExercisesSketch the graph of the function, based on the basic graphs in Section 5.1 and the transformations described above. Find the formula of the function that is given by performing the following transform...Sketch the graph of the function, based on the basic graphs in Section 5.1 and the transformations described above. Find the formula of the function that is given by performing the following transformations on the graph. shifted to the right by \(3\) (to get the graph of \(y=\dfrac{1}{x}\) ) and then reflected about the \(x\)-axis compressed towards the \(x\)-axis by a factor \(2\) (you get \(y=|x|\)) then shifted to the left by \(1\) and up by \(1\)
