How do you find the linearization at a=1 of #f(x)=x^(3/4)#?
It is the equation of the tangent line at
so the linearization is
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To find the linearization at ( a = 1 ) of ( f(x) = x^{3/4} ), follow these steps:

Find the derivative of ( f(x) ): ( f'(x) = \frac{3}{4}x^{1/4} ).

Evaluate ( f'(1) ) to find the slope of the tangent line at ( x = 1 ): ( f'(1) = \frac{3}{4} ).

Use the pointslope form of a line to find the equation of the tangent line at ( x = 1 ): [ y  f(1) = f'(1)(x  1) ].

Substitute ( f(1) = 1^{3/4} = 1 ) and ( f'(1) = \frac{3}{4} ) into the equation: [ y  1 = \frac{3}{4}(x  1) ].

Simplify the equation to get the linearization at ( a = 1 ): [ y = \frac{3}{4}x  \frac{1}{4} ].
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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