Linearization and Differentials Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Find the linearization at given

(2) Find the linearization at given

(3) Find the linearization at given

(4) Find the linearization at given

(5) Find the linearization at given .

(6) Find the linearization at given

(7) Find the linearization at given

(8) Use linearization to approximate the function at

(9) Use linearization to approximate the function at

(10) Show that the linearization of at is for a constant

(11) Find the linearization of at How is it related to the individual linearizations of and at

(12) Find the differential of the function

(13) Find the differential given

(14) Find the differential of the function

(15) Find the differential of the function

(16) Find the differential of the function   

(17) Find the differential of the function   

(18) In exercises 19-21 each function changes value when changes from to Finish labeling the following diagram and use it for exercises 19-21. What are the four distances the arrows are representing? Also label the two lines which are dashed by finding an equation for each line.

(19) Given and find the change and the value of the estimate

(20) Given and find the change and the value of the estimate

(21) Given and find the change and the value of the estimate

(22) Write a differential formula that estimates the change in the volume of a sphere when the radius changes from to

(23) Write a differential formula that estimates the change in the lateral surface area of a right circular cone when the radius changes from to

(24) Find the differential of the function

(25) Find the differential of the function

(26) Use differentials to find an approximate value for the real number

(27) Use differentials to find an approximate value for the real number

(28) Use differentials to find an approximate value for the real number

(29) Find the linearization of the function at

(30) Find the linearization of the function at

(31) Find the linearization of the function at

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