Calculus Answers

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),__,__,____,_______,

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.

A function is defined on R such that f(x) = (C^2)x when x≤1 and 5Cx-6 when x>1 . Determine the values of C so that f becomes continues on R

trace the curve , x^2= y^2((x+1)^3 ) , stating all the points used in process

Evaluate the following

"n\\sum i=1 (3\/2^(i-1))"

When creating a left-endpoint Riemann sum on the interval [-29.8, 388.8] using 26 rectangles, the 7th endpoint used to calculate the height of the approximating rectangle would be? Calculate the following showing all your steps.

The following function is continuous at x = 0:

𝑓(𝑥) =

(1−cos𝑘𝑥)/(xtanx)

, 𝑓𝑜𝑟 𝑥 ≠ 0 𝑎𝑛𝑑 𝑓(0) = 3. find k.