Search
- Filter Results
- Location
- Classification
- Include attachments
- https://math.libretexts.org/Courses/Penn_State_University_Greater_Allegheny/MATH_110%3A_Techniques_of_Calculus_I_(Gaydos)/01%3A_Review/1.03%3A_Linear_FunctionsLinear functions can always be written in the form \[f(x)=b+mx\nonumber \] or \[f(x)=mx+b\nonumber \] where \(b\) is the initial or starting value of the function (with input \(x = 0\)), and \(m\) is ...Linear functions can always be written in the form \[f(x)=b+mx\nonumber \] or \[f(x)=mx+b\nonumber \] where \(b\) is the initial or starting value of the function (with input \(x = 0\)), and \(m\) is the constant rate of change of the function.
- https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_2160%3A_Applied_Calculus_I/02%3A_Exponential_and_Logarithmic_functions/2.02%3A_Exponential_FunctionsSince \(b = 1 + r = 1.64\), we know that every quarter the number of smart phone contracts grows by 64%. \(T(2) = 231.3056\) means that in the second quarter (or at the end of the second quarter) ther...Since \(b = 1 + r = 1.64\), we know that every quarter the number of smart phone contracts grows by 64%. \(T(2) = 231.3056\) means that in the second quarter (or at the end of the second quarter) there were approximately 231,305 Android smart phone contracts. The graph of \(k(x)\) is the easiest to identify, since it is the only equation with a growth factor less than one, which will produce a decreasing graph.
- https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_2160%3A_Applied_Calculus_I/03%3A_Applications_of_Differentiation/3.03%3A_OptimizationCalculus provides ways of drastically narrowing the number of points we need to examine to find the exact locations of maximums and minimums, while at the same time ensuring that we haven’t missed any...Calculus provides ways of drastically narrowing the number of points we need to examine to find the exact locations of maximums and minimums, while at the same time ensuring that we haven’t missed anything important.
- https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_2160%3A_Applied_Calculus_I/06%3A_Algebra_Review
- https://math.libretexts.org/Bookshelves/Calculus/Applied_Calculus_(Calaway_Hoffman_and_Lippman)/00%3A_Front_Matter/04%3A_IntroductionSince then, thousands of other men and women have refined the basic ideas of calculus, developed new techniques to make the calculations easier, and found ways to apply calculus to problems besides pl...Since then, thousands of other men and women have refined the basic ideas of calculus, developed new techniques to make the calculations easier, and found ways to apply calculus to problems besides planetary motion. Chapter 2 The Derivative builds on the precalculus idea of the slope of a line to let us find and use rates of change in many situations.
- https://math.libretexts.org/Courses/Penn_State_University_Greater_Allegheny/MATH_110%3A_Techniques_of_Calculus_I_(Gaydos)/01%3A_Review/1.07%3A_Exponential_FunctionsSince \(b = 1 + r = 1.64\), we know that every quarter the number of smart phone contracts grows by 64%. \(T(2) = 231.3056\) means that in the second quarter (or at the end of the second quarter) ther...Since \(b = 1 + r = 1.64\), we know that every quarter the number of smart phone contracts grows by 64%. \(T(2) = 231.3056\) means that in the second quarter (or at the end of the second quarter) there were approximately 231,305 Android smart phone contracts. The graph of \(k(x)\) is the easiest to identify, since it is the only equation with a growth factor less than one, which will produce a decreasing graph.
- https://math.libretexts.org/Bookshelves/Calculus/Applied_Calculus_(Calaway_Hoffman_and_Lippman)/01%3A_Review
- https://math.libretexts.org/Courses/Penn_State_University_Greater_Allegheny/MATH_110%3A_Techniques_of_Calculus_I_(Gaydos)/02%3A_The_Derivative/2.03%3A_Power_and_Sum_Rules_for_DerivativesThe average variable cost is the total variable cost divided by the number of items, so we would divide the $25,000 total variable cost by the 200 items made. $25,000/200 = $125. On this graph, that i...The average variable cost is the total variable cost divided by the number of items, so we would divide the $25,000 total variable cost by the 200 items made. $25,000/200 = $125. On this graph, that interval is too small to see, and our best guess at the secant line is actually the tangent line to the TC curve at that point. (This is the reason we want to have the derivative definition handy.)
- https://math.libretexts.org/Courses/Penn_State_University_Greater_Allegheny/MATH_110%3A_Techniques_of_Calculus_I_(Gaydos)/04%3A_Functions_of_Two_VariablesPoints with the same elevation are connected with curves, so you can read not only your east-west and your north-south location, but also your elevation. You may have also seen weather maps that use t...Points with the same elevation are connected with curves, so you can read not only your east-west and your north-south location, but also your elevation. You may have also seen weather maps that use the same principle – points with the same temperature are connected with curves (isotherms), or points with the same atmospheric pressure are connected with curves (isobars). In this chapter, we will use that same idea to make graphs of functions of two variables.
- https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_2160%3A_Applied_Calculus_I/04%3A_The_Integral/4.05%3A_Area_Average_Value_and_VolumeThat's because for the triangle on the right, the graph of \(y = x\) is above the graph of \(y = 3\), so the integrand \(3 - x\) is negative; in the definite integral, the area of that triangle comes ...That's because for the triangle on the right, the graph of \(y = x\) is above the graph of \(y = 3\), so the integrand \(3 - x\) is negative; in the definite integral, the area of that triangle comes in with a negative sign. The volume of the solid obtained by rotating about the \(x\)-axis the area bounded by the curve \(f(x)\), the \(x\)-axis, \(x = a\), and \(x = b\) is \[ \int_a^b \pi\left(f(c_i)\right)^2\, dx \nonumber \]
- https://math.libretexts.org/Courses/Chabot_College/MTH_15%3A_Applied_Calculus_I/05%3A_The_Integral/5.08%3A_Applications_to_BusinessLet \(P\) be the principal (initial investment), \(r\) be the annual interest rate expressed as a decimal, and \(A(t)\) be the amount in the account at the end of \(t\) years. The idea here is that ea...Let \(P\) be the principal (initial investment), \(r\) be the annual interest rate expressed as a decimal, and \(A(t)\) be the amount in the account at the end of \(t\) years. The idea here is that each little bit of income in the future needs to be multiplied by the exponential function to bring it back to the present, and then we'll add them all up (a definite integral).
