Math Answers

For each of these pairs of sets, determine whether the first is a subset of the second, the second is a subset of the first, or neither is a subset of the other

9) Use your value of x to calculate a value for 𝑒𝑥 from the first four

terms.

X = 1

lim log x

𝑥→1

x ,0.5, 0.9 ,0.99 ,0.999

f(x),__,__,____,_______,

x ,1.5 ,1.01 ,1.001, 1.0001

f(x),__,__,____,_______,

a random sample of size n 16 is drawn from a normally distributed population. the sample mean is 98 with known standard deviation of 5. Construct a 98% confidence interval for the population mean.

Water is being poured at the rate of 15cm3/sec into an inverted cone with a diameter of 3m and a 

height of 6m. At what rate is the surface rising just as the tank is filled?

A trough is 75cm long and its ends in the form of an isosceles triangle have an altitude of 20cm 

and a base of 30cm. Water is flowing into the trough at the rate of 100cm3/sec. Find the rate at 

which the water level is rising when the water is 10cm deep?

A trough is 75cm long and its ends in the form of an isosceles triangle have an altitude of 20cm 

and a base of 30cm. Water is flowing into the trough at the rate of 100cm3/sec. Find the rate at 

which the water level is rising when the water is 10cm deep?

How can you find the absolute difference between the left and right riemann sum on a closed interval? Provide an example with your reasoning.

Define W =  x y  : xy ≥ 0  . Decide if V is a vector space or notand prove your claim. (Hint: V is the union of the first and third quadrants in the xyplane)

Define W =

 x

y



: xy ≥ 0



. Decide if V is a vector space or notand prove

your claim. (Hint: V is the union of the first and third quadrants in the xyplane)