sssgggg2827 sssgggg2827
  • 02-12-2017
  • Mathematics
contestada

Find a formula for the function f(x) such that f′(x)=(ln(x))^2/x and f(2)=6

Respuesta :

chudung1976
chudung1976 chudung1976
  • 02-12-2017
f(x)= ∫ln²x/x dx= ∫ln²xd(lnx) cause d(lnx)= (lnx)'dx=1/x dx
= ln³x/3 +C with C is constant
In addition, we have f(2)=6, so we have 6=ln³2/3+C
or C= 6- ln³2/3
And f(x)= 
ln³x/3+  6- ln³2/3
Answer Link

Otras preguntas

Do you think email marketing is more or less effective than more traditional types of marketing?
What is 4x+5+5x9+9+9(3+5)-10x20
what is 1 3/4 + 2 2/3 equal to?​
Write a question tag for the following statements. 1. Let's study tomorrow, ? 2. Write an email, ? 3. Everybody clapped, ? 4. A little cream is added to the d
One common theme throughout both of the regions that we have recently discussed is aridity. True False
Alex wants 2 hoodies, he wants to know which one is bigger. A. Measurements : 29" (74 cm) length, 27" (69 cm) bust B. Measurement: 28" (71 cm) length, 26" (66
30 points!!! Find the area of each. Round to the nearest tenth. Do not include units in your answer (ie. ft, in, km, etc)(triangle-FR) *
Name and describe five ways in which plants can respond to stimuli
Write an equation for the line parallel to the given line that contains C. C(4,8); y=-3x+1
Select the correct answer. How many degrees are there in a right angle? 90° 180° 270° 360°