# Calculus

Calculus
A particle is moving with acceleration a(t) = 24 t + 4. Its position at time t =0 is s(0) = 15 and its velocity at time t =0 is v(0) = 11. What is its position at time t = 9?

Calculus - Differential Equations
Use separation of variables to find the solution to the differential equation: 4 (du/dt) = u^2, subject to the initial condition u(0)=6. So far, I have: 4 du = u^2 dt 4/u^2 du = dt -4/u = t+C I am unsure what to do from this point...

Calculus - Falling Body Problem
Near the surface of the earth, the acceleration of a falling body due to gravity is 32 feet per second per second, provided that air resistance is neglected. If an object is thrown upward from and initial height of 3000 feet with a velocity of 75 feet per second, find its ...

Calculus - Differential Equations
Use separation of variables to find the solution to the differential equation: 4 (du/dt) = u^2, subject to the initial condition u(0)=6.

Calculus
Find the xy-equation of the curve that passes through (-2, -2) and whose slope at any point on the curve is equal to 5 times the x-coordinate of that point

Calculus
An offshore oil well is 4 kilometers off the coast. The refinery is 5 kilometers down the coast (see figure). Laying pipe in the ocean is twice as expensive as on land. What path should the pipe follow in order to minimize the cost?

calculus
Consider a window the shape of which is a rectangle of height h surmounted by a triangle having a height T that is .3 times the width w of the rectangle If the cross-sectional area is A, determine the dimensions of the window which minimize the perimeter. h = w =

Calculus
A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An industrial tank of this shape must have a volume of 1600 cubic feet. The hemispherical ends cost twice as much per square foot of surface area as the sides. Find the dimensions that ...

Calculus
Sketch the given region R and then find its area. R is the region bounded by the curve y=1/x^2 and the lines y=x and y=x/8.

Calculus
A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An industrial tank of this shape must have a volume of 1600 cubic feet. The hemispherical ends cost twice as much per square foot of surface area as the sides. Find the dimensions that ...

calculus
Cars on a certain roadway travel on a circular arc of radius r. In order not to rely on friction alone to over­ come the centrifugal force, the road is banked at an angle of magnitude 0 from the horizontal. The banking angle must satisfy the equation rg tan 0 = v^2 where v is...

calculus
A patrol car is parked 50 feet from a long warehouse The light on the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall when the beam makes the fol­ lowing angles with the line perpendicular from the light to the wall? (a)=30...

Calculus
If f(x) = 2xsqrt(x-6), what is the value of (f^-1)(40)?

calculus
A point is moving along the graph of y = x2 so that dx/dt is 2 centimeters per minute. Find dy/dt when (a)x = 0 and (b)x = 3.

Calculus
All edges of a cube are expanding at the rate of 3 centimeters per second. How fast is the volume chang­ ing when each edge is (a) 1 centimeter and (b) 10 centimeters?

calculus
At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at the rate of 10 cubic feet per minute. The diameter of the base of the cone is approx­ imately three times the altitude. At what rate is the height of the pile changing when it is 15 feet high?

Calculus
A spherical balloon is inflated with gas at the rate of 20 cubic feet per minute. How fast is the radius of the balloon increasing at the instant the radius is (a) 1 foot and (b) 2 feet?

Calculus
Find the dot product of: <-1, 7> and <2, ¾>.

Calculus
A plane traveling 500 mph (called airspeed) in the direction 120 degrees encounters a wind of 80 mph in the direction of 45 degrees. What is the resultant direction of the plane (in degrees)?

Calculus
Given ||v|| = 5 theta=30 degrees, write the vector v.

Calculus
What is the unit vector of v: <-6, -8>?

Calculus
Find the particular solution that satisfies the differential equation and the initial conditions. F'(x) = 4x^2 f (-1)=3 F'(t)=10t-12t^3 f (3)=2

Calculus
A 5ft tall person is walking toward a light 20ft off the ground at 8 ft/sec. What is the rate of change of the length of the persons shadow when they are 15ft away from the light? What is the speed of the tip of the shadow moving?

Calculus
True or False If F(x) and G(x) are antiderivatives of f(x), then F(x)=G(x)+C If f'(x) = g(x) then integral g(x) dx = f(x) + C Integral f(x) * g(x)dx = integral f(x)dx * integral g(x)dx I have a feeling it's False True True

Calculus
Find the particular solution that satisfies the differential equation and the initial conditions. f''(x) = x^2 f'(0) = 8, f(o)=4 f'(t) 10t - 12t^3, f(3) =2

Calculus
Find the points on the lemniscate, given below, where the tangent is horizontal 2(x^2 + y^2)^2 = 49(x^2 − y^2)

Calculus
Find dy/dx at the point (-3, 1) for the equation x = y^3-9y^2+5. A. -1/17 B. -1/13 C. -1/15 D. 1/17 E. 1/15 I posted this question before with a typo, but the point still doesn't appear to be on the graph of the function.

Calculus
Find dy/dx at the point (-3, 1) for the equation x = y^3-9x^2+5.

pre calculus
A rectangular parcel of land has an area of 4,000 ft2. A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel. What are the dimensions of the land, correct to the nearest foot?

calculus
find the economical proportion between the radius and height of the cylindrical can to give the least dimensions of a metal that encloses vloume of 10cu.in

Calculus
The measurement of the circumference of a circle is found to be 70 centimeters, with a possible error of 0.9 centimeter. a) Approximate the percent error in computing the area of the circle. (Round your answer to two decimal places.) b) Estimate the maximum allowable percent ...

Calculus
The velocity of an object is given by v(t)=t(t^2-1)^(1/3) feet per second. Find the total number of feet traveled by the object in the time interval [0,3] seconds. (A)51/4 (B)34/3 (C)45/4 (D)51/8 (E)45/8

calculus
indefinite integral : (sqrt(V^2sin^2(2pi/T*t))) dt

Calculus differentiable and continous identify
1. Which of the above functions are not continuous where they are defined? Why? 2. Which of the above functions are not differentiable where they are defined? Why? Photo Link: goo.gl/photos/2RPU1dAWoKzUn4Pf8 For the first question, I said that graph F is not continuous because...

Calculus AB
Um I don't really understand these word problems so could someone help me please? 1) An object is thrown upward with an initial velocity of 5 m/s from an initial height of 40 m. Find the velocity of the object when it hits the ground. Assume that the acceleration of gravity is...

Calculus AB
Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x-1)e^x. For which value of x is the slope of the tangent line to f positive? Negative? Zero? 2) Find an equation of the tangent line to the oven curve at the specified point. Sketch the curve and the...

Pre-Calculus
Why do we need to use the sum/difference formulas to find exact values? Please explain.

Calculus AB
Could someone please help me with this? Calculate the instantaneous rate of change of f <note: f(x)=(x-6)/(x+6)> at x=6.

Calculus
Use the limit process to find the area of the region between the graph of the function and the y-axis over the given y-interval. f(y) = 7y, 0 ≤ y ≤ 2

Calculus
Determine an upper/lower estimate for the area under the curve f(x) = cos x between x = 0 and x = pi/2 . Show how you arrive at this estimate. This is the question that my teacher wanted us to answer and I'm not sure how to even start the process. Should I use Reimann's Sum? ...

Business Calculus
As the financial consultant to a classic auto dealership, you estimate that the total value (in dollars) of its collection of 1959 Chevrolets and Fords is given by the formula v = 306,000 + 1,000t2 (t ≥ 5) where t is the number of years from now. You anticipate a ...

Calculus
Given the vectors u = <−3, 7> and v = <5,1>, find 3u + 2v.

Calculus
Given the vectors u = <−3,7> and v = <5,1>, find -½ u. A. <-1,-4> B. <-4,-1> C. <3/2,-7/2> D. <-3/2,7/2>

Calculus
Find d^2y/dx^2 in terms of x and y given that 8x + 6y^2 = 8. Use the original equation to simplify your answer. A. y'' = -(4/9y^3) B. y'' = -9y^3 C. y'' = -4y^3 D. y'' = -27y^3 E. y'' = -(8/27y^3)

Calculus I
(Six pigpen problem). A 2 × 3 array of six congruent rectangular pigpens (that all look the same from above) will be in the overall shape of a rectangle R. We may use 100 feet of fencing to form the boundaries of the pigpens. Find the dimensions for a single pigpen that will ...

Calculus
How to derive cosh (3x) in terms of cosh (x) and sinh (x) ? Initially I start with 1/2 (e^3x+e^-3x) but I'm stuck from there because I don't know how to continue... :(

calculus
need help in below question. Thanks. A man runs round a circular track at a constant speed. Would like to know how to drawn locus of the points representing the magnitude ‘d’ of the displacement of the man from the starting position against time ‘t’ , during one lap of...

ab calculus
Air is being blown into a spherical balloon at the rate of 75 cm3/s. Determine the rate at which the radius of the balloon is increasing when the radius is 28 cm.

calculus
A car is traveling west at 67 mi./hr and a truck is traveling south at 59 mi./hr. Both are headed for the intersection of the two roads. At what rate are the car and truck approaching each other when the car is 0.2 mi. and the truck is 0.5 mi. from the intersection?

Differential calculus
Differentiate the following y=root(e^x)/x

Differential calculus with analytic geometry
use implicit differentiation to find dy/dx. xy^2+4y^3=x-2y

Calculus
Find the equation of the tangent line to the curve 2x^2y-3y^2=-11 at the point (2,-1).

College Calculus
If a ball is thrown vertically upward from the roof of 48 foot building with a velocity of 96 ft/sec, its height after t seconds is s(t)=48+96t−16t^2. What is the maximum height the ball reaches? What is the velocity of the ball when it hits the ground (height 0)?

Calculus
A particle moves according to the equation of motion s(t)=t^2-2t+3 where s(t) is measured in feet and t is measured in seconds. Find the total distance traveled in the 3 seconds.

Calculus
Starting at t=0, a particle moves along the x-axis so that its position at time t is given by x(t)=t^4-5t^2+2t. What are all values of t for which the particle is moving to the left? (A)0<t<0.913 (B)0.203<t<1.470 (C)0.414<t<0.913 (D)0.414<t<2.000 (E)...

Calculus
Find the slope of x^2-16xy+y^2=1 at (1,1). Is this -1?

Calculus (AC)
Steve, you've been an amazing help. Thank you so much. This is the last question I need checked. Solve ∜82 using differentials. I got 3.00926

Calculus (answer check)
The measurement of the radius of a circle is 16 inches, with a possible error of .25 inches. (Use differentials to approximate the possible propagated error and the percent error. Propagated error= 1.6% Percent error= 4.6%

Calculus
The measurement of the radius of a circle is 16 inches, with a possible error of .25 inches. Use differentials to approximate the possible propagated error in computing the area of the circle and find the percent error. I've gotten to 2Pi*16*.25 but don't know what to do past ...

Calculus
The function f is given by f(x)=3x^2+1. What is the average value of f over the closed interval [1,3]? The answer I get is 12, but the book says it's 14. I don't understand why.

math calculus
A poster is to contain 300 (cm square) of printed matter with margins 10cm at the top and bottom and 5cm at each side. Find the overall dimensions if the total area of the poster is minimum.

Calculus
Ship A is moving east at 20 miles per hour, while ship B is moving north at 15 miles per hour. At noon ship A was 5 miles east of an island, and ship B was 75 miles south of the island. At what rate is the distance of the ships changing at 1 pm?

Math (Calculus)
Determine if each of the following functions is in Big-O, is Big-Omega and is Big-Theta of x: (Could be multiple) a) f(x)=10 b) f(x)=3x+7 C) f(x)=x^2+x+1 d) f(x)=5log(x) e) f(x)=|x| f) f(x)=x/2 I'm in calc 1 and I have no idea what's it even asking me. Help? Thanks in advance!

Calculus
An error in the measurement of the radius of a circle results in an error in the computation of its area. Find and interpret the sensitivity of area (a) of a circle to the measurement of radius, r, when the radius r=2 meters.

Calculus
Can you please help me find the x and y intercepts of this equation. How do I solve this? y= x^2 √9-x^2

CALCULUS
if F(x) = f(xf(xf(x))),where f(1) = 4, f(4) = 6, f '(1) = 4, f '(4) = 5,and f '(6) = 6,find F '(1).

calculus
Union membership as a percentage of the labor force can be modeled by M(x) = 0.0003x3 − 0.066x2 + 4.64x − 81, where x is the number of years after 1900,and M is membership as a percentage of the labor force. a. Find the rate at which membership is changing in 1960...

Math (Calculus)
Determine if each of the following functions is in Big-O, is Big-Omega and is Big-Theta of x: (Could be multiple) a) f(x)=10 b) f(x)=3x+7 C) f(x)=x^2+x+1 d) f(x)=5log(x) e) f(x)=|x| f) f(x)=x/2 I'm in calc 1 and I have no idea what's it even asking me. Help? Thanks in advance!

Calculus 2
A spring has a natural length of 25 meters. A force of 12 newtons is required to stretch the spring to a length of 30 meters. How much work is done to stretch the spring from it's natural length to 40 meters? -I forgot to add the 40 meters part to my other question here is ...

calculus 2
A spring has a natural length of 25 meters. A force of 12 newtons is required to stretch the spring to a length of 30 meters. How much work is done to stretch the spring from it's natural length?

Calculus
Let f be a function with second derivative given by f''(x)=sin(2x)-cos(4x). How many points of inflection does the graph of f have on the interval [0,10]? (A)Six (B)Seven (C)Eight (D)Ten (E)Thirteen

Calculus
differentiate the given function, simplify your answer by leaving no negative or rational exponents. final answer should be in factored form where possible. y=(x^2 +2x)^3(x+2)

Calculus
A nut store sells 200 bags of almonds per month at a price of \$5 per bag. For every \$0.20 decrease in the price, the store sells five more bags per month. Determine the marginal revenue when 120 bags are sold.

Calculus
f(x, y) = 3ycos x, 0 ≤ x ≤ 2π Finding the locla minima, maxima, and saddle points. Having difficulty as so far I have: Fx = -3ysinx Fy = 3cosx Fxx = -3ycosx Fyy = 0 Fxy = -3sinx I have set both Fx and Fy equal to 0 but am not too sure about the critical points...

Calculus
A nut store sells 200 bags of almonds per month at a price of \$5 per bag. For every \$0.20 decrease in the price, the store sells five more bags per month. Determine the marginal revenue when 120 bags are sold.

Calculus
The demand function for a bottle of hand lotion is p(x)=0.78+0.0003x, where x is the number of bottles sold and p is the price, in dollars. The cost function is c(x)=480-0.32x+0.0005x^2. Find the marginal profit when 700 bottles of hand lotion are sold.

Calculus
Determine the coordinates of the point on the graph of f(x)=3x^2-7x+4 where the tangent line is parallel to the line 5x+y=3

Calculus
find the point, (c,f(c)), on f(x)=x^2 in the interval 0≤X≤4, such that f'(c) equals the average rate of change over that interval.

Calculus
Determine the equation of the tangent to f(x)= (1/x)+x at the point (1,2)

calculus
lim f(x)=? x->3- f(x); -3.7, -3.97, -3.997, -3.9997, ?

calculus
Locate the discontinuities of the function y=(5)/(3+e^(1/x))

Calculus
The function f is continuous on the open interval (-π, π). If f(x)=cos(x)-1/xsin(x) for x≠0, what is the value of f(0)?

Calculus
A water trough is 5 m long and has a cross-section in the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 70 cm wide at the top, and has height 40 cm. If the trough is being filled with water at the rate of 0.2 m3/min how fast is the water level rising when ...

Calculus integrals
(e^(3x)-2e^(2x)+(5e^x))/(e^x+1) how do I do this what is the techniques??

Calculus
A right circular cone has a volume of cubic inches. What shape should it be in order to have the smallest lateral surface area? Find the result of the volume is V cubic inches.

Calculus
A right circular cone has a volume of 100 cubic inches. What shape should it be in order to have the smallest lateral surface area? Find the results of the volume is V cubic inches.

Calculus
Let f be a differentiable function defined on the closed interval [a,b] and let c be a point in the open interval (a,b) such that I.f'(c)=0 II.f'(x)>0 when a≤x<c III.f'(x)<0 when c<x<≤b Which of the following statements must be true? (A)f(c)=0 (B)f"(...

Calculus
If the functions f and g are defined for all real numbers and f is an antiderative of g, which of the following statements is NOT necessarily true? (A)If g(x)>0 for all x, then f is increasing (B)If g(a)=0, then f(x) has a horizontal tangent at x=a (C)If f(x)=0 for all x, ...

calculus
A running circuit is to be constructed in the shape of a rectangle with two semicircles attached at the east and west ends of the path (see figure). A picnic area will be set in the center of the circuit. If we want the total length of the circuit to be 2000 m (2km ), what ...

calculus
A printed page is to have 1 in. margin on all sides. The page should contain 80 sq. in. of type. What dimensions of the page will minimize the area of the page while still meeting the other requirements?

Calculus
Suppose f(x) and g(x) are functions of x differentiable at x = 4. Given that f(4) = 3, f'(4) = -2, g(4) = 6, g'(4) = -5, find the value of each of the following. a. Derivative of f(x) * g(x) My answer: -27 b. Derivative of (f(x))/(g(x)) My answer: 1/12 c. Derivative of (g(x...

calculus
5.In a certain state the maximum speed permitted on freeways is 65 km/h and the minimum speed is 40 km/h. The fine for violating these limits is Rs.15 for every kilometer per hour above the maximum speed or below the minimum speed. Express the amount of the fine as a function ...

calculus
For each of the following limits, determine the indicated limit if it exists. lim f(x)=? x approaches 4 from the left f(x)= -3.9997

Calculus
Suppose f(x) and g(x) are functions of x differentiable at x = 4. Given that f(4) = 3, f'(4) = -2, g(4) = 6, g'(4) = -4, find the value of each of the following. a. Derivative of f(x) * g(x) My answer: -27 b. Derivative of (f(x))/(g(x)) My answer: 1/12 c. Derivative of (g(x...

Calculus
A baseball team plays in a stadium that holds 68000 spectators. With the ticket price at \$11 the average attendence has been 27000. When the price dropped to \$10, the average attendence rose to 34000. Assume that attendence is linearly related to ticket price. What ticket ...

Calculus
I need help determining whether the following functions are even, odd, or neither. Please help me. 1. f(x)=4x+5 2. f(x)=x^3-x-2 3. f(x)=x^4-x / x^5-x 4. f(x)= x^3-x / x^5

Calculus
Lim (√(3-x) - √(3+x)) /x x->0

Calculus
Lim √(3-x) - √(3+x) x->0 x

Integrals calculus
7/x^2-8 does it give you 7ln(x^2-8)

calculus
(Compute all instantaneous rate of change using the limit of the difference quotient) 2) A football's path is represented by the function h(t)=-4.9t^2 +10t+2, where h is its height, in meters, after t seconds. Find the rate of change of the football's height at 1s.