For the function in this problem, approximate by computing with .
A)-0.0171
B)0.2730
C)-1.0325
D)-0.0483
E)0.0537

Question

For the function in this problem, approximate  by computing  with  . ​  ​
A)-0.0171 
B)0.2730 
C)-1.0325 
D)-0.0483 
E)0.0537

Quizplus · Accepted Answer

To approximate a value using differentials, we use the formula:

f(x + delta x) ≈ f(x) + f'(x) * delta x

In this case, we want to approximate f(11eb0d3b_9842_1040_9790_b545b12704c5_TB1243_11) using f(11eb0d3b_9842_1042_9790_fd58e0860f4a_TB1243_11) and f'(11eb0d3b_9842_1041_9790_bb19bdef0627_TB1243_11) = -0.0483.

So, we have:

f(11eb0d3b_9842_1040_9790_b545b12704c5_TB1243_11) ≈ f(11eb0d3b_9842_1042_9790_fd58e0860f4a_TB1243_11) + f'(11eb0d3b_9842_1041_9790_bb19bdef0627_TB1243_11) * (11eb0d3b_9842_1040_9790_b545b12704c5_TB1243_11 - 11eb0d3b_9842_1042_9790_fd58e0860f4a_TB1243_11)

Plugging in the values, we get:

f(11eb0d3b_9842_1040_9790_b545b12704c5_TB1243_11) ≈ f(11eb0d3b_9842_1042_9790_fd58e0860f4a_TB1243_11) + (-0.0483) * (11eb0d3b_9842_1040_9790_b545b12704c5_TB1243_11 - 11eb0d3b_9842_1042_9790_fd58e0860f4a_TB1243_11)

f(11eb0d3b_9842_1040_9790_b545b12704c5_TB1243_11) ≈ 0.2730 + (-0.0483) * (-4) ≈ -0.0171

Therefore, the best choice is D, -0.0171.

For the Function in This Problem, Approximate by Computing