((1/(15^(15/16))+15^(1/16)?

👨🏻‍🏫 學術台數學

[匿名]

2017-10-17 10:21 pm

更新1:

((1/(15^(15/16))+(15^(1/16)? this is originally a natural log problem that I broke down to get the above. The purpose was to a) Find the open interval(s) on which the function is increasing and decreasing. b. Identify the function's local and absolute extreme values, if any, saying where they occur. I know the answer in decimal. I just don't get how to manipulate the fractions/powers to get the actual answer in fractions ---- (16)/((15^(15/16))

回答 (6)

DWRead

2017-10-17 10:27 pm

✔ 最佳答案

What is the question?
Also, the parentheses are unbalanced so I can't tell what the expression is supposed to be. Is the 15^(1/16) part of the denominator?

👍 2 👎 0

wanszeto

2017-10-17 10:39 pm

[1/15^(15/16)] + [15^(1/16)]
= [1/15^(15/16)] × [15^(1/16)/15^(1/16)] + [15^(1/16)] × (15/15)
= [15^(1/16)/15] + [15×15^(1/16)/15]
= (16/15)[15^(1/16)]

👍 3 👎 0

用戶55769

2017-10-18 12:14 am

((1/(15^(15/16)) + 15^(1/16)
= 1.26338125030272734...

👍 0 👎 0

2017-10-17 11:22 pm

Very close to 9229/7305.

👍 0 👎 0

cidyah

2017-10-17 10:36 pm

Let x = (15)^(15/16)
log x = (15/16) log(15)
log x = (15/16) (1.17609126) = 1.10259
x = 10^1.10259
x = 12.66456

((1/(15^(15/16)) = 1/12.66456 = 0.07896

Let y = 15^(1/16)
log y = (1/16) log(15)
log y = 1.17609126 /16 =0.07351
y = 10^0.07351 = 1.18443

x+y = 1.26339

👍 0 👎 0

Captain Matticus, LandPiratesInc

2017-10-17 10:35 pm

1 / 15^(15/16) + 15^(1/16) =>
(1 + 15^(16/16)) / 15^(15/16) =>
(1 + 15) / 15^(15/16) =>
16 / 15^(15/16) =>
16 * 15^(-15/16)

👍 0 👎 0

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