Linearization

What is the linearization function L(x) for f(x) = sin(x) for values of x near 0?

• L(x) = x
• L(x) = x + 1
• L(x) = sin(x) + x cos(x)
• L(x) = cos (x) (x - 0)

What is the linearization function L(x) for
y = (2x-1)² for values of x near 3?

• L(x) = 20x - 35
• L(x) = (2x - 1)² (x - 3)
• L(x) = -4x + 1
• L(x) = 4(2x - 1)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Let L(x) = 3(x - 4) - 2.  Find L(3.9).

• -1.7
• -2.3
• 1
• 2.3

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

Find dy for the function y = cos(x).

• dy = -sin(x) 
• dy = -sin(x) dx
• dy = cos (x) dx
• dy= cos(x) 

Find dy for the function y = 4x² + x + 3.

• (8x² + x + 3)dx
• (4x + 1)dx
• (8x + 1)dx
• 8x + 1

Find dy if dy/dx = 7 and dx = 1/2. 

• 7/2
• 14
• 1/14
• 2/7

Find dy for 2xy² - x² + y = 5 if x = 0 and dx = 0.01. 

• -50
• -0.5
• -5
• (2x - 2y²) / (4xy + 1) dx

Let f(x) = x³.  Find f(1) and f(1.1).  Calculate ∆f.

• 1
• 1.331
• 0.331
• -0.331

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

Let f(x) = x³.  L(x) is the linearization of f(x) centered at x = 1.  Calculate df if ∆x = 0.1. 

• 0.1
• 3
• 0.3
• 1.3

Tags

CCSS.HSF.IF.C.7

Let f(x) = x³ and L(x) be the linearization of f(x) centered at x = 1. Calculate the approximation error when ∆x = 0.1. 

• 0.1
• 0.01
• 0.331
• 0.031

Tags

CCSS.HSF.IF.C.7