Find the Linearization at a=16 f(x)=x^(1/2) , a=16

Math
,
Consider the function used to find the linearization at .
Substitute the value of into the linearization function.
Evaluate .
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Replace the variable with in the expression.
Simplify .
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Remove parentheses.
Simplify the expression.
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Rewrite as .
Apply the power rule and multiply exponents, .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
Find the derivative and evaluate it at .
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Find the derivative of .
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Differentiate using the Power Rule which states that is where .
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
Move the negative in front of the fraction.
Rewrite the expression using the negative exponent rule .
Multiply and .
Replace the variable with in the expression.
Simplify.
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Simplify the denominator.
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Rewrite as .
Multiply the exponents in .
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Apply the power rule and multiply exponents, .
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Use the power rule to combine exponents.
Add and .
Raise to the power of .
Substitute the components into the linearization function in order to find the linearization at .
Simplify.
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Simplify each term.
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Apply the distributive property.
Combine and .
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Subtract from .
Write in form.
Find the Linearization at a=16 f(x)=x^(1/2) , a=16

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