Sabrina Ayon, a Computer Science and Engineering graduate from United International University, has been an integral part of the ExcelDemy project for two years. She authored 150+ articles, excelling in instructing through visually engaging Excel tutorials. With a passion for teaching, Sabrina conducte...
Thus, in view of (3), exp is strictly increasing and concave-up on ℝ. (5) We have the following standard integral. ∫expxdx=expx+C,∫exdx=ex+C. Example 15.2.3 Find (a) ddxetan x, (c) ∫ e3x − 5dx. Solution (a) Using the chain rule, ddxetanx = etanx sec2x. (b...
Fig. 2. Scheme of steam zone cross section in the Reis model (Reis, 1992). Exploiting Butler's idea and the application of HIM (Heat Integral Method) in converting the energy balance PDE equation into a solvable ODE one and finding the heat diffusion depth ahead of oil–steam interface in...
In this section, we shall discuss the basic definitions with properties of some significant and applicable special functions. Special Functions As stated in the introduction, for getting the analytical solution from a differential equation with the application of Laplace integral transformation, the Laplac...
−∞ −∞ (11) Mathematics 2019, 7, 920 5 of 14 Subintegral function is greater than zero only for values T• > B, so we get (12): ∞φ(B) = T• E(T) f (T•) 1 T• dT• = 1 − F(B) E(T) S (12) T where F(T) is distribution function of the ...
NOTE: The numbers on the y-axis become too close together near each integral power of 10, so they have been removed for readability. Example 1: Graph of y=xy=x Let's see what the simple graph y=xy=x looks like on different axis types. a. y=xy=x on Linear Axes On ordinary lin...