Reference no: EM131076893
MATH 1A MIDTERM 2-
Problem 1- (i) State Rolle's Theorem.
(ii) State the Mean Value Theorem.
(iii) Prove the Mean Value Theorem. You may assume Rolle's Theorem.
Problem 2- In each of the following cases, evaluate dy/dx.
(i) y = sin(x) ln |x|.
(ii) y = x2/cos x
(iii) y = (10x4 - 5)20
(iv) y = sin(x sin x)
(v) y = tan(x2)ex^3
(vi) y4x - 3y = e2x (you should leave your answer in terms of y and x)
Problem 3- Showing your working carefully, calculate dy/dx when y = xe^x. Give your answer in terms of just x.
Problem 4- I start with 5 ties to wear on special occasions. My hair-dresser tells me that my separation anxiety is because I don't have enough nice clothes. Taking the advice to heart, I start shopping and my tie collection starts to grow exponentially. After 3 days I have 12 ties. How long will it be before I have 100 ties? You do not need to simplify or evaluate your answer.
Problem 5- Which point on the graph of y = √x is closest to the point (4, 0)?
Problem 6- A salt crystal is growing in a super-saturated solution of salt. It is a perfect cube and its length, width and height are all growing at a rate of 1 mm per day. What is the rate of increase of the volume of the cube when its length, width and height all equal 10 mm?
Problem 7- Showing your working carefully, evaluate
limx→0(sin2(x)/4x2).
If you use a rule to change the limit, then you should name that rule each time you use it.
Problem 8- What is 9log497?
Determining the equation for motion of the object
: An object is thrown up from a height h = 9.8 m with velocity of 4.9 m/s. Derive the equation for motion of the object starting from the force equation. Show each step and find the time at which it reaches ground and it's speed when it hits the grou..
|
Consider a sequential search of n data items
: Consider a sequential search of n data items.
|
Discuss what you believe to be the origins of animals
: Consider three (3) problems out of control population growth will create in regards to the environment. Next discuss three (3) effects of China's one child rule. In your response please consider social, ethical and environmental sides of the effec..
|
Discuss significance of strategic marketing planning process
: Discuss the significance of value throughout strategic marketing planning process. Developing marketing strategy is more importantthan implementing marketing strategy because if the strategy is flawed, itsimplementation doesn't matter.
|
What is the rate of increase of the volume of the cube
: MATH 1A MIDTERM 2. A salt crystal is growing in a super-saturated solution of salt. It is a perfect cube and its length, width and height are all growing at a rate of 1 mm per day. What is the rate of increase of the volume of the cube when its le..
|
Masses on the ends as point masses
: What is the magnitude of the angular momentum of the system taking the center of the rod as the origin? Treat the masses on the ends as point masses.The answer is in kg*m^2/s.
|
How many comparisons does f perform
: Consider the following C++ function f , which calls the function swap . Assume that swap exists and simply swaps the contents of its two arguments. Do not be concerned with f s purpose.
|
Determining the frictionless horizontal surface
: A 1.00kg block slides with a speed of 0.880m/son a frictionless horizontal surface until it encounters a spring with a force constant of 450N/m. The block comes to rest after compressing the spring 4.15 cm.
|
Do you have any other ideas to reinforce proper policing
: Quotes Walker et al. (2007) and their position on racism in the CJ system. The following paragraph discusses strategies to overcome barriers based on race and suggests "zero tolerance policies on bias within the police ranks." While this sounds li..
|