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Basic Calculus

Various calculus problem set

Please see the attached file for complete description 1. Write the first five terms of the arithmetic sequence: a1 = 3; d = 3 2. A spinner is used for which it is equally probable that the pointer will land on any one of six regions. Three of the regions are colored red, two are colored green, and one is colored yellow. If t

Continuity, Differentiability and the Volume of a Solid

Please see attached file for full problem description. 1. Decide whether each of the following statements is true or false. If true, explain why. If false, give a counter-example and explain why the counter-example contradicts the statement. a. If then b. If f and g are continuous functions on [a,b], then c. If f

Third Prime

Please help, figured out first two primes but am having allot of problems figuring out the third prime. Also need help with additional problem. Thanks Find lim x ->∞ ( (3x-2) / (3x+2) )^x (3x - 2)^x / (3x+2)^x = lim x ->∞ f'(x)/g'(x) x(3x - 2)^(x-1)*(3)/ x(3x-2)^(x-1)*(3) =(3x - 2)^(x-1)/ (3x

2 Objective questions

Please choose the correct answer: ∫ 12x(x - 2)^10 dx = x^12 + (24/11)x^11 + C x^12 + (2/11)x^11 + C (12/11)(x - 2)^11 + C (12/11)x(x - 2)^11 + c (x - 20/11)(x - 2)^11 + C (x + 2/11)(x - 2)^11 + C none of these b

2 objective questions

13. Find the area under the curve y = 3e^-x - e^x , from x = 0 to x = ln(3)/2. 3 - 2(2^1/2 ) 4 - 2(3^1/2 ) 1 6 - 2(5^1/2 ) 7 - 2(6^1/2 ) none of these 14. Calculate, correct to the nearest hundredth, 2.25 ∫(2.73x^2 - 8.41x + 7) dx = 0.5

Calculus Questions

Q#11. The graph of y=f(x)=x^2 + 2x is shown in the graph. i) Find the slope of the secant line joining (2, f(2)) and (4, f(4)). ii) Find the slope of the secant line joining (2, f(2) and (2+h, f(2+h)) _____ + _____ h Q#12. Suppose an object moves along the y axis so that its locations is y=f(x)=x^2+3x at time x(y

Given a region R bounded by the curve y = x^2-2x and the x-axis, we have to find the position of the object x(t) at time t. Also, we have to find the position of the object at time t = 4. Given the position of the object, we have to find the time at which it was at x = 3. The solution involved the integral calculus. For complete description of the problem, please see the problem.

1. R is the region bounded by the curve y = x^2 -2x and the x axis. Sketch the given region R and then find its area. 2. Using the following integral and the facts that v(t) = x'(t) at time t of an object moving along the x axis is given, along with the initial position x(0) of the object. Answer the questions a - c. x'

Exponential Population Growth

The population P of a city is given by P = 2000e^kt . Let t=0 correspond to the year 1960 and suppose the population in 1950 was 1500. Find the value of k ( to 3 decimal places) and then predict the population in 2000. Please show all steps & graph, solve using derivatives or ln on calc.

Related Rates

3.A pulley is suspended 13.5 m above a small bucket of cement on the ground. A rope is put over the pulley. One end of the rope is tied to the bucket and the other end dangles loosely to the ground. A construction worker holds the end of the rope at a constant height (1.5 m) and walks away from beneath the pulley at 1.6 m/s. How

General solution and Particular solution of Differential Equation, Vectors , Radius of Circle and Center of Circle, Initial Value problem. For complete description of the problems, please see the posted problems.

Question (1) First find a general solution of the differential equation dy/dx=3y. Then find a particular solution that satisfies the initial condition that y(1) = 4 Question (2) Solve the initial value problem dy/dx=y^3 , y(0) = 1 Question (3) Find the centre and radius of the circle described in the equation 2x2 + 2

Work Done in Compression

A force of 650 pounds compresses a spring 5 inches from its natural length. Find the work done in compressing the spring 2 additional inches. Answer in inch-pounds.

Continuity and the Intrmediate Value Theorem

Suppose that f is continuous on [a,b], f(z) < 0, and f (b) > 0. Set z = sup{x: f (t) < 0 for all t contained in [a, x]}. Prove that f (z) = 0. This is key to the proof of the intermediate value theorem. Incorporate the definition of least upper bound into your argument.

Uniformly Continuous

Let E be a nonempty subset of R and f:E-->R. State the definition f is uniformly continuous on E. Prove f(x) =x^2 is uniformly continuous on the interval[0,1]. keywords: uniform continuity

Math precalculus graphing calculator project

The purpose of this project is to find the values of x and y that will yield the optimum (maximum or minimum) value of a system and the optimum value of a system using algebraic and graphical methods. Follow these ten steps (see mp1.jpg) to determine the optimum value of z and the values of x and y that yield the optimum valu

Calculus Functions

The following table shows the average number of hours worked per week at a place of... Calculus Functions. See attached file for full problem description.

Angular Displacement

The flywheel of a gasoline engine rotates at an angular speed of 3240 rpm. Find its angular displacement (in revolution) in 10 sec.

Transportation Cost

For speeds between 40 and 65 mph, a truck gets 480/x miles per gallon when driven at a constant speed of x miles per hour. Diesel gasoline costs 2.23 per gallon, and the driver is paid 15.10 per hour. What is the most economical constant speed between 40 and 65 miles per hour at which to drive the truck.

Buoyancy and Terminal Velocity

Archimedes principal of buoancy states that an object submerged in a fluid is buoyed up by a force equal to the weight of the fluid the object displaces. A rectangular box 1foot X 2 feet X 3 feet and weighing 384 lbs. is dropped into a 100 foot deep freshwater lake (density 62.4 lbs/cubic foot). The box immediately begins to

Velocity, Time and Displacement

A stone is dropped from a high cliff and falls with velocity v = 32t feet per second. How many feet does the stone travel during the first 3 seconds?

Using Rectangles to Approximate Area

Use rectangles to approximate the area bounded by the graph of the function f(x) = x3, the x-axis, and the lines x = 0 and x = 2. Use n = 4 subintervals.

Width of Subintervals

If we break the interval from x = -1 to x = 1 into n = 4 subintervals, what is the width of each subinterval?

Advance Engineering Maths

Please show steps on how you get the answer, type out if possible for easy reading. (See attached file for full problem description)