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seiferseph
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Here is the problem I'm having some trouble with. The answer is fairly simple, it is the power of the e function. (the parabola x = y^2 + 1) I'm not sure how to get that, i could use some hints/help, thanks!
benorin said:I'll be kind: recall that [tex]e^w \geq 1[/tex] if, and only if, [tex]w\geq 0,[/tex] that is, if, and only if the exponent of e is greater than or equal to 0. You are asked to find (and sketch) all points in xy-plane (e.g. all values of x and y) such that [tex]e^{1-x+y^{2}}\geq 1,[/tex] which occurs if, and only if, [tex]1-x+y^{2}\geq 0[/tex] which describes the region in the xy-plane bounded by (and to the left of) the parabola [tex]x=1+y^{2}[/tex].
A multivariable sketch problem involves solving a mathematical equation or function that has multiple variables. This means that the equation or function has more than one independent variable and requires you to consider the relationships between these variables in order to find a solution.
The power of e function, also known as the exponential function, is a mathematical function of the form f(x) = ex, where e is a constant approximately equal to 2.71828. This function is commonly used in many fields of science and mathematics, including calculus, statistics, and physics.
To solve a multivariable sketch problem involving the power of e function, you will need to first identify all of the independent variables and their relationships within the equation. Then, you can use algebraic techniques and the properties of the power of e function to manipulate the equation and solve for the desired variable.
The power of e function has many real-life applications, including modeling population growth, compound interest, and decay processes. It is also commonly used in physics to describe the relationship between a varying force and a particle's displacement.
One helpful tip for solving these types of problems is to carefully consider the properties of the power of e function, such as the chain rule and the fact that ex is its own derivative. It can also be useful to graph the equation or function to visualize the relationships between the variables and their behavior. Additionally, practicing with different types of multivariable sketch problems can help improve your problem-solving skills in this area.