Find the linearizations of

a. tan x at x = -π...

Question

Find the linearizations of

a. tan x at x = -π/4

Graph the curves and linearizations together.

Accepted Answer

Find the linearization of the function F of X equals Z X and X equals 0. Then graph F of X and its linearization in the same rectangular coordinate system. Now, we're also given a graph here to plot our equations on. Now, to answer this, let's first find the linearization. The linearization is given by the equation L of X. equals F of A. Plus if primly. X minus a In our case, We can first find F of A, which will just be F of 0. That's E to the 0 or just 1. Now we also need F of A. F X is just eats the X. So if we want F of A. This will be E to the 0. Which is also just one. We can now plug everything into our linearization function. L 0 Equals one. Plus 1 multiplied by X minus 0. This simplifies to 1 plus X. Now that we have our linearization function, let's graph our function eats the X. We will find Values Or eats the X. Let's say we choose. F of -2. This is E to the negative second power, which is approximately 0.14. We keep finding points that are close to 0. Like, say, X equals -1, we would get E to the negative first, is approximately 0.37. F of 1 It's east of the first, which is approximately 2.72. And finally F of 2 Which is each of the 2nd or approximately. 7.39. We can now plot this on. Our graph. We have the points, -2. 0.14 1, 0.37. 01 1 2.72. And 2 7.39. Let's go ahead and plot these. We have negative 2. 0.14 1, 0.37, 01. 1 2.72. And 2 7.39. Finally, we just need to make a curve between our points to graph E to the X. And there we have our function he of the X. Now let's graph the linearization. Now we know our linearization. Is the equation 1 + X, and if we choose points such as X equals 0, We would get the points, out of 0. Equals 1 + 0, which gives us 1 or 0.1. If we choose X equals 1, we get L of 1, equals 1 + 1 or 2, giving the 0.12. We can graph this on the same plane. We have 01. And 12. We just seem to draw a straight line between these two points. This gives us our linearization function, LX equals 1 plus X, and now we have both of our functions on the graph. OK, I hope to help you solve the problem. Thank you for watching. Goodbye.

Find the linearizations of

a. tan x at x = -π/4

Graph the curves and linearizations together.

Key Concepts

Linearization

Derivative of Trigonometric Functions

Graphing Functions and Linear Approximations

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