How do you find the linearization at a=1 of #f(x) = 2 ln(x)#?
I hope that this was clear.
By signing up, you agree to our Terms of Service and Privacy Policy
To find the linearization of ( f(x) = 2 \ln(x) ) at ( a = 1 ), follow these steps:
-
Find the first derivative of ( f(x) ): [ f'(x) = \frac{2}{x} ]
-
Evaluate the derivative at ( x = a = 1 ): [ f'(1) = \frac{2}{1} = 2 ]
-
Find the value of ( f(a) ): [ f(1) = 2 \ln(1) = 2 \cdot 0 = 0 ]
-
Use the formula for the linearization: [ L(x) = f(a) + f'(a)(x - a) ]
-
Substitute the values of ( f(a) ), ( f'(a) ), and ( a ) into the formula: [ L(x) = 0 + 2(x - 1) ]
-
Simplify: [ L(x) = 2x - 2 ]
So, the linearization of ( f(x) = 2 \ln(x) ) at ( a = 1 ) is ( L(x) = 2x - 2 ).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided 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 one-sided 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 one-sided 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 one-sided 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.
- At what rate, in cm/s, is the radius of the circle increasing when the radius is 5 cm if oil is poured on a flat surface, and it spreads out forming a circle and the area of this circle is increasing at a constant rate of 5 cm2/s?
- If a hose filling up a cylindrical pool with a radius of 5 ft at 28 cubic feet per minute, how fast is the depth of the pool water increasing?
- The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the diameter is 40 mm?
- Stevie completes a quest by travelling from #A# to #C# vi #P#. The speed along #AP# is 4 km/hour, and along #AB# it is 5 km/hour. Solve the following?
- How do you find the rate at which water is being pumped into the tank in cubic centimeters per minute if water is leaking out of an inverted conical tank at a rate of 12500 cubic cm/min at the same time that water is being pumped into the tank at a constant rate, and the tank has 6m height and the the diameter at the top is 6.5m and if the water level is rising at a rate of 20 cm/min when the height of the water is 1.0m?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7