[Notes & HW Answers] 3.9 Linear Approximation

[Notes & HW Answers] 3.9 Linear Approximation.pdf

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[Prepwork 3.9]

Q1. What is the value at x=.1 of the local linearization L(x) of (1+x)^5 at x=0?

A: L(0.1) = 1.5

Q2. Suppose you use the tangent line approximation near t=4 to estimate s′(4.05), where s(t) is a function that is always concave up. Then your answer is an

A: underestimate

Q3. Suppose the linear approximation of g(x)g(x) near x=6 is given by L(x)=5(x−6)−12.

A:Then g(6) = -12 and g'(6) = 5.

[HW 3.9]

Q1. Find the tangent line approximation for (4+x)^(1/2) near x = 0.

A: y= 2+ (1/4)x

Q2. Near x=0, the tangent line approximation gives 2e−5x≈

A: 2-10x 

Q3. Suppose f′(x) is a differentiable increasing function for all x. In each of the following pairs, which number is the larger?
For each, enter A or B.

A: 1. Comparing A. f'(9) and B. f'(10): B is larger.

2. Comparing A. f''(9) and B.0: A is larger.

3. Comparing A. f(9+Δx) and B. f(9) + f'(9)Δx: A is larger.