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Lesson Worksheet: Linear Approximation Mathematics • Higher Education

In this worksheet, we will practice using derivatives to find the equation of the line that approximates the function near a certain value and using differentials to approximate the change in the function.

Q1:

Find the linear approximation of the function 𝑓(π‘₯)=π‘₯βˆ’π‘₯+3 at π‘₯=βˆ’2.

  • Aπ‘₯βˆ’8
  • B6π‘₯+3
  • C16π‘₯+23
  • D16π‘₯+32
  • E16π‘₯βˆ’9

Q2:

Find the linear approximation of the function 𝑓(π‘₯)=√π‘₯ at π‘₯=4.

  • Aπ‘₯βˆ’2
  • B14π‘₯+1
  • C14π‘₯βˆ’1
  • D14π‘₯+2
  • E12π‘₯

Q3:

What is the tangent line approximation 𝐿(π‘₯) of √1βˆ’π‘₯ near π‘₯=0?

  • A1βˆ’βˆšπ‘₯2
  • B1+π‘₯2
  • C1βˆ’π‘₯2
  • D1βˆ’π‘₯2
  • E1+π‘₯2

Q4:

Find the linear approximation of the function 𝑓(π‘₯)=√π‘₯ at π‘₯=βˆ’8.

  • A112π‘₯+23
  • Bβˆ’2π‘₯βˆ’19112
  • C14π‘₯βˆ’4
  • D112π‘₯βˆ’2
  • E112π‘₯βˆ’43

Q5:

Find the linear approximation of the function 𝑓(π‘₯)=π‘₯π‘₯+1 at π‘₯=1.

  • A14π‘₯+14
  • B14π‘₯+12
  • C12π‘₯βˆ’14
  • D14π‘₯βˆ’14
  • E12π‘₯

Q6:

Find the linear approximation of the function 𝑓(π‘₯)=π‘₯sin at π‘₯=πœ‹6.

  • Aβˆ’βˆš32π‘₯+√3πœ‹12+12
  • Bπ‘₯βˆ’πœ‹6+12
  • C√32π‘₯βˆ’βˆš3πœ‹12+12
  • D√32π‘₯βˆ’βˆš3πœ‹12
  • E√32π‘₯+12

Q7:

Find the linear approximation of the function 𝑓(π‘₯)=π‘₯π‘₯sin at π‘₯=2πœ‹.

  • A2πœ‹π‘₯+4πœ‹οŠ¨
  • Bβˆ’2πœ‹π‘₯+4πœ‹οŠ¨
  • Cπ‘₯βˆ’2πœ‹
  • D2πœ‹π‘₯βˆ’4πœ‹οŠ¨
  • E2πœ‹π‘₯

Q8:

Find the linear approximation of the function 𝑓(π‘₯)=π‘₯sin at π‘₯=0.

Q9:

Find the linear approximation of the function 𝑓(π‘₯)=π‘₯tan at π‘₯=πœ‹.

  • Aπ‘₯
  • B0
  • Cπ‘₯+πœ‹
  • Dπ‘₯βˆ’πœ‹
  • Eπœ‹βˆ’π‘₯

Q10:

Find the linear approximation of the function 𝑓(π‘₯)=2 at π‘₯=0.

  • Aπ‘₯+2ln
  • Bπ‘₯2+1ln
  • Cπ‘₯2ln
  • Dπ‘₯2+1ln
  • Eπ‘₯+1

This lesson includes 27 additional questions for subscribers.

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