QQuestionMathematics
QuestionMathematics
"Find the linearization L(x) of f(x)equalstangent x at xequalspi.
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Part 1
The linearization is given by L(x) equals"
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Answer
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Step 1:: Recall the formula for the linearization of a function f(x) at a point x=a.
L(x) = f'(a)(x-a) + f(a)
The formula is:
Step 2:: In this problem, we are given f(2$) = tan(2$) and we need to find the linearization at x=π.
To do this, we first need to find f'(π).
Step 3:: Find the derivative of f(2$) = tan(2$).
The derivative of tan(2$) is sec^2(x). So, f'(x) = sec^2(x).
Step 4:: Evaluate f'(π).
We know that sec(2$) = - 1, so f'(π) = sec^2(π) = (- 1)^2 = 1.
Step 5:: Now we need to find f(π).
The value of tan(π) is 0.
Step 6:: Substitute the values into the formula for linearization:
L(x) = f'(π)(x-π) + f(π) = 1(x-π) + 0
Step 7:: Simplify the expression:
L(x) = x - π
Final Answer
The linearization L(x) of f(2$) = tan(2$) at x = π is L(x) = x - π.
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