Find the linear approximation of the function g(x) = 5 1 + x at a = 0. g(x) ≈ use it to approximate the numbers 5 0.95 and 5 1.1
. (round your answers to three decimal places.) 5 0.95 ≈ 5 1.1 ≈ illustrate by graphing g and the tangent line. webassign plot webassign plot webassign plot webassign plot
1 answer:
Differentiating the function
... g(x) = 5^(1+x)
we get
... g'(x) = ln(5)·5^(1+x)
Then the linear approximation near x=0 is
... y = g'(0)(x - 0) + g(0)
... y = 5·ln(5)·x + 5
With numbers filled in, this is
... y ≈ 8.047x + 5 . . . . . linear approximation to g(x)
Using this to find approximate values for 5^0.95 and 5^1.1, we can fill in x=-0.05 and x=0.1 to get
... 5^0.95 ≈ 8.047·(-0.05) +5 ≈ 4.598 . . . . approximation to 5^0.95
... 5^1.1 ≈ 8.047·0.1 +5 ≈ 5.805 . . . . approximation to 5^1.1
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Answer:
25 ft
Step-by-step explanation:
The diagram shows two triangles that are similar. Similar triangles have equal angles and sides that are proportional to each other. Since the base of each triangle is given, we can find the proportion of the sides:
Given the ratio of the smaller to larger triangle, we can set up a proportion to find the missing height of the larger triangle:
, where 'x' represent the height of the tree
cross-multiply: x = (5)(5) or 25 ft