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Chapter 21: Problem 6

If \(f(x, t)=\mathrm{e}^{2 x}\) find \(f(0.5,3)\).

Short Answer

Expert verified
Answer: The value of the function at x = 0.5 and t = 3 is e.

Step by step solution

01

Identify the function

The given function is: \(f(x, t) = \mathrm{e}^{2x}\)
02

Plug in the values

Insert the values x = 0.5 and t = 3 into the function: \(f(0.5, 3) = \mathrm{e}^{2(0.5)}\)
03

Simplify and solve

Simplify the exponent: \( \mathrm{e}^{2(0.5)} = \mathrm{e}^{1}\) Now, evaluate the exponential function with an exponent of 1: \(f(0.5, 3) = \mathrm{e}^{1} = e\) So, the function evaluated at \(f(0.5, 3)\) equals e.

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Most popular questions from this chapter

In each case, given \(z=f(x, y)\) find \(z_{x}\) and \(z_{y}\). (a) \(z=x y\) (b) \(z=3 x y\) (c) \(z=-9 y x\) (d) \(z=x^{2} y\) (e) \(z=9 x^{2} y\) (f) \(z=8 x y^{2}\)

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$$ \text { If } w=5 y-2 x \text { state } \frac{\partial^{2} w}{\partial x^{2}} \text { and } \frac{\partial^{2} w}{\partial y^{2}} \text {. } $$
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