Linear Approximation

Linear Approximation

12th Grade

20 Qs

quiz-placeholder

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Linear Approximation

Linear Approximation

Assessment

Quiz

Mathematics

12th Grade

Hard

Created by

Anthony Clark

Used 1+ times

FREE Resource

20 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Suppose f(x) = x3 – x.

Use a linear approximation at x = 2 to estimate f(2.5).

10.5

11

11.5

12

2.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

4.6

4.7

4.8

4.9

3.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

f(4) = 1
f'(4) = 3
Using a linear approximation centered at 4, f(4.5) ≈

5/2

3/2

4/3

7/3

4.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

f(x) = x2(x+1)2
Which of these is the linear approximation to f centered at x = 1?

L(x) = 12x - 1

L(x) = 6x + 5

L(x) = 12x - 8

L(x) = 12x - 16

5.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

f(x) = x-2/5
Use a linear approximation centered at x = 32 to approximate (30)-2/5.

17/180

25/64

23/128

41/160

6.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Which of the following represents the linear approximation to f (x) at the point (c, f(c)) ?

L(x) = f'(c) + f(c)(x - c)

L(x) = f(c) + f'(c)(x - c)

L(x) = f'(c) + f(c)(x + c)

L(x) = f(c) - f'(c)(x - c)

7.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

How can we minimize the error of an approximation in a linear approximation at the point (a, f (a))?

By translating the point of tangency in either direction

By restricting the values of f (x) sufficiently close to f (a)

By iterating further away from the point of tangency

By restricting the values of x sufficiently close to 'a'

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