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Homework Statement
(2sinx - 5e^x)
The Attempt at a Solution
is it just...
-2cosx - 5e^x
The function 2sin(x) - 5e^x is a combination of a sine function and an exponential function. It is used to model many natural phenomena, including periodic oscillations and growth/decay processes.
The graph of 2sin(x) - 5e^x can be plotted by first graphing the individual functions of sin(x) and e^x, and then adding or subtracting their corresponding y-values at each point on the x-axis.
The important features of the graph of 2sin(x) - 5e^x include the x-intercepts, where the function crosses the x-axis, and the maximum and minimum points, where the function reaches its highest and lowest values. The period and amplitude of the sine function and the rate of growth/decay of the exponential function can also be observed on the graph.
The derivative of 2sin(x) - 5e^x can be calculated using the rules of differentiation. The derivative of sin(x) is cos(x) and the derivative of e^x is e^x, so the derivative of the entire function is 2cos(x) - 5e^x.
The function 2sin(x) - 5e^x has many real-world applications, including modeling the movement of a pendulum, the behavior of a spring, and the growth/decay of populations in biology. It can also be used to analyze data in fields such as economics and engineering.