Calculus Answers

A stone is thrown vertically upward from the ground with an initial velocity of 40 ft/sec. 

 What is the height of the ball when its velocity is one-half the initial velocity?

Determine the half-life of the radioactive substance

Three cars arrive simultaneously at a four way stop and all want to proceed straight through the intersection. How many ways are there for this to happen if they proceed on at a time. Show a diagram with your explanation.

A cone of radius r centimetres and height h centimetres iss lowered first at a rate of 1 cm/s into a tall cylinder of radius R that is partially filled with water. How fast is the water level rising at the instant the cone is completely submerged?

Sketch the graph of f(x)=|x| where x belongs to R, state it domain and range.

Let f: R->R be defined by f(x)=x²+2 where R is the set of real numbers

(i) find the domain and range of f

(ii) is f one-to-one or onto ?

A baseball player is running from the second base to the third base at 20ft/sec. At what rate is his

distance from the home plate changing when he is 30ft from the third base. The baseball diamond

is a square 90ft on aside.

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),__,__,____,_______,