In April 2025
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find lim x----> 1-x ^3/infinity x+1
state the statement is true or false the function f[x,y]={x^2y/x^4+y^2[x,y]=0 is not continuous at [0,0] and 0,[x,y]=0
Use the bissection method to approximate the root of f(x)=2x²-1 in the interval . Let ε=0.1 be the margin of error of approximation.
Calculate the surface area Integral of object obtained by rotating the function x=2y+5 for x=-1 and -2 about y axis
(1) At the start, an experiment records 1 gram of bacterial culture, and the culture’s weight is believed to have a carrying capacity of 12 grams.
(6.1) Find a model for the weight of the bacterial culture as a function of time t. ?
(6.2) If, after 4 hours, the culture weighs 8 grams, find the weight after 10 hours.?
If c>0, then the following equality holds,
the integral from a to b dx/x equals to the integral from ac to bc dx/x.
Show your work and an explanation for each step.
F(x) = "\\smallint" "(x+9)dx \/ (x-2)(x+2)"2 and F(3.1) = 5.5. Compute F( -0.5)
A projectile is launched vertically upward from the ground level with an initial velocity of 16 ft/s.
a. How long will it take for the projectile to hit the ground?
b. How long will the projectile be moving upward?
A boy in a hot air balloon drops his cellular phone when the balloon is 150 ft above the ground and rising at the rate of 10 ft/s.
a.How long will it take the cellular phone to reach the ground?
b. With what speed will it strike the ground?
of 10 genes studied in yeast, 7 are found to form a network of metabolic interactions. If this set of 7 genes was chosen arbitrarily from the 10 that were studied, how many different sets would be possible? Show your calculation and the reasoning.a
