Linear Approximation

Quiz
•
Mathematics
•
12th Grade
•
Hard
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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