# Calculus

Pre-Calculus
A population of 20 rabbits is introduced to a small island. The population increase at a rate of 60% per year. (A) Find a function of F(t) that represents the number of rabbits on the island after t years. (B) Suppose 100 rabbits were introduced to the island and G(t) is the ...

Calculus
The sum of two positive numbers is 10. Find the numbers if their product is to be a maximum

Applied calculus
A geologist in Tibet discovers a new mountain in the area of Gyangtse. The equation of the mountain is given by f(x,y) = -x^4 - y^4 +2xy where x and y is measured in mile. What is the relative maximum height of the mountain in meters?

calculus
At an Oregon fiber-manufacturing facility, an analyst estimates that the weekly number of pounds of acetate fibers that can be produced is given by the function : z=f(x,y)=1250ln(yx^2)+45(y^2+x)(x^3 -2y)-(xy)^1/2 where z= the weekly # of pounds of acetate fiber produced x=the...

calculus
At an Oregon fiber-manufacturing facility, an analyst estimates that the weekly number of pounds of acetate fibers that can be produced is given by the function : z=f(x,y)=1250ln(yx^2)+45(y^2+x)(x^3 -2y)-(xy)^1/2 where z= the weekly # of pounds of acetate fiber produced x=the...

calculus
At an Oregon fiber-manufacturing facility, an analyst estimates that the weekly number of pounds of acetate fibers that can be produced is given by the function : 2 2 3 ( , ) 1250ln( ) 45( )( 2 ) z f x y yx y x x y xy       where...

calculus
A balloon is now stuck at a tree 280meters away from the ground. The balloon is observed by the crew of boat as they look upward at an angle of 25 degrees. Twenty-five seconds later, the crew has to look at an angle of 65 degrees to see the balloon. How fast was the boat ...

LIMITS CALCULUS
lim (cubic root (7+x^2-8x^3)/(x^3-x+pi)) x--> +inf I don't know how to take the limit when there is a cubic root around . Between the ansswer is + inf . I need direction

Pre-Calculus
Find the equation in standard form for the hyperbola that satisfies the given conditions: transverse axis endpoints (-2,-2) and (-2,7), slope of one asymptote 4/3. I found the distance of the transverse axis to be 9. For the formula, I have a=9/2. I need help finding h, k, and...

Pre-Calculus
Find the equation in standard form for the hyperbola that satisfies the given conditions: transverse axis has endpoints (5,3) and (-7, 3) and conjugate axis has a length of 10. I found the distance of the transverse axis to be 12. For the formula, I have a=6 b=5. I just need ...

Pre-Calculus
For any two linear functions f(x)=ax+b and g(x)=cx+d, is f o g the same as g o f?

Calculus
Consider the region in the plane consisting of points (x, y) satisfying x > 0, y > 0, and lying between the curves y=x^2 +1and y=2x^2 −2. (b) Calculate the area of this region.

calculus
sin(cos^-1(x/2))= draw right triangle to simplify

Integral calculus
Use the cylindrical shell method to find the volume of the solid generated by revolving the area bounded by the given curves (x-3)^2 + y^2 = 9, about y-axis.

calculus question ?
I just can't wrap my head around this. I don't know if this is true I just came to conclusion with this if the limit of x--> +/-inf = L (if the limit of x going to pos/neg infinity gives you a number L) does that mean that L is a horizontal asymptote ? if the limit of x---a...

calculus
Find the area of the region bounded by the graph of f(x)=x(x+3)(x+1) and the x-axis on the interval [-3,0]

pre calculus
The population of foxes in a certain region over a 2-year period is estimated to be P1(t) = 300 + 50 sin(πt/12) in month t, and the population of rabbits in the same region in month t is given by P2(t) = 4000 + 400 cos(πt/12) . Find the rate of change of the ...

Differential Calculus
A clock has hands 1 and 1 3/5 inches long respectively. At what rate are the ends of the hands approaching each other when the time is 2 o'clock?

Calculus
A particle moves along the curve y=lnx so that its abscissa is increasing at a rate of 2 units per second. At what rate is the particle moving away from the origin as it passes through the point (1,e)?

calculus
Use implicit differentiation to find dy/dx if 384,000=30x^1/3y^2/3 .

Calculus
A searchlight revolving once each minute is located at a distance of 1/4 mile from a straight beach. How fast is the light moving along the beach when the beam makes an angle of 60° with the shore line?

calculus
A fertilizer producer finds that it can sell its product at a price of p=300-x dollars per unit when it produces x units of fertilizer. The total production cost (in dollars) for x units is C(x)= 20,000+24x+0.5x^2. How many units must be manufactured to maximize the profit?

Pre Calculus
The following table shows the rate of water flow (in L/min) through a dam. t (min) 1 5 9 13 17 21 25 V'(t) (L/min) 6 6 2 2 3 6 2 Approximate the total volume of water that passed through the dam from t=1 to t=25 using Simpson's rule, with n=6.

calculus 1
Set up the simplified integral and compute the volume created when the area bounded by y=.25x4, y=4, and the y=axis (Quadrant 1) is rotated around the line x=-2

calculus
Set up the simplified integral and compute the volume created when the area bounded by one period of the function 3+sin(x) and the x-axis (use the endpoints of the period starting at x=0) is rotated around: a) the x-axis b) the y-axis

Differential Calculus
The base of an isosceles triangle is 10 feet long and the base angles are decreasing at a rate of 2° per second. Find the rate of change of the area when the base angles are 45°.

Calculus
The base of an isosceles triangle is 8 feet long. If the altitude is 6 feet long and is increasing 3 inches per minute, are what rate are the base angles changing?

Calculus
A building is to be braced by means of a beam which must pass over a wall. If the wall is 3 3/8 feet high and stands 8 feet from the building, find the shortest beam that can be used.

Calculus
A statue 10 feet high is standing on a base 13 feet high. If an observer's eye is 5 feet above the ground, how far should he stand from the base in order that the angle between his lines of sight to the top and bottom of the statue be a maximum?

Calculus
Find the area of the largest rectangle cut from the first quadrant by a line tangent to the curve y=e^(-x^2)

Calculus
Using l'hopitals rule, evaluate the following: Lim x-->infinity Inx/2(x)^1/2 Limx-->0 (1/x - 1/e^x -1) I tried both multiple times and I'm still not getting an answer. For the first one I tried l'hopitals rule 3 times and I'm still getting infinity over infinity for an ...

calculus
The volume V, in liters, of air in the lungs during a two-second respiratory cycle is approximated by the model V = 0.1729t + 0.1522t^2 − 0.0374t^3, where t is the time in seconds. Approximate the average volume of air in the lungs during one cycle. (Round your answer to...

calculus sir damon help me or steve
integrate dx/root(coshx-1) plz show step

Calculus
Let x µ = x µ (u) be a parametric equation for the curve in pseudo-Riemannian four-space connecting points P and Q. Here u is any, not necessarily affine parameter. Assume that the derivative satisfies Update: Let x µ = x^µ(u) be a parametric equation for the curve in ...

calculus
Find dy/dx. y = x^ln x, x > 0

calculus
1. A rocket is fired vertically into the air. Six kilometers away, a telescope tracks the rocket. At a certain moment, the angle between the telescope and the ground is and is increasing at a rate of 0.6 radians per minute. (See the picture. I have defined y to be the height ...

math: pre-calculus
You have 5 grams of carbon-14; whose half-life is 5730 years. a)Write the rule of the function that gives the amount of carbon-14 remaining after x years. b)How much carbon-14 will be left after 4,000 years? c)When will there be just 1 gram left?

math: pre-calculus
Solve the equation. First express your answer in terms of natural logarithms (for instance, z=(2+ln5)/ln3). Then use a calculator to find an approximation for the answer. 3^x+9=2^x.

math: pre-calculus
If current rates of deforestation and fossil fuel consumption continue, then the amount of atmospheric carbon dioxide in parts per million (ppm) will be given by f(x)=375e^0.00609c, where c=0 corresponds to 2000. a)What is the amount of carbon dioxide in 2022? b)In what year ...

math: pre-calculus
Solve the equations. Log(6x-1) = Log(x+1) + log4

math: pre-calculus
Let u=lnx and v=lny. Write the expression ln3√x/2y in terms of u and v. For example, lnx^3y=lnx^3+lny=3lnx +lny= 3u+v.

math: pre-calculus
Write the expression as a single logarithm. Ln(e^3y)+ln(ey)-4

math: pre-calculus
Let u=ln and v=ln y. Write the expression ln(5√(x3√y)) in terms of u and v. for example, lnx^3y = lnx^3+lny = 3lnx+lny = 3u+v

math: pre-calculus
For the log function (h(x)=log(x+3)-8): a) Find the domain. b) Find the asymptotes. c) Find the x-intercepts.

math: pre-calculus
List the transformations that will change the graph of g(x)=lnx into the graph of the given function h(x)=log(x+3)-8 a) Horizontally shift the graph to the right by 3; then vertically shift downward by 8. b) Horizontally shift the graph to the left by 8; then vertically shift ...

math: pre-calculus
Evaluate the expression without using a calculator. Unless stated otherwise, all letters represent positive numbers. e^(ln√x+5)

math: pre-calculus
The Department of Commerce estimated that there were 53 million internet users in the country in 1999 and 90 million in 2002. Find an exponential function that the models the number of Internet users in year x, with x=0 corresponding to 1999.

math: pre-calculus
5. For the log function (h(x)=log(x+3)-8): a) Find the domain. b) Find the asymptotes. c) Find the x-intercepts.

Calculus
using implicit differentiation find the equation of the tangent line to the graph of the following function at the indicated point x^2 y^3 -y^2+xy-1=0 at (1,1)

Calculus
Water is draining from a swimming pool in such a way that the remaining volume of water after t minutes is V = 200(50 - t)^2 cubic meters. Find : (a) the average rate at which the water leaves the pool in the first 5 minutes

calculus
Find the limit lim x ->0 (sin^2 2x)/(x^2)

calculus
evaluate the definite integr 2 ∫ (x+1/x)² dx 1

calculus
the marginal cost function for widgets is dr/dq= 0.001Q^2+0.01Q+10 total fixed xosts equal \$500 part 1= convert the marginal cost function into total cost function. part 2= determine total costs when Q=100.

calculus
evaluate the definite integrals 1 ∫ root(1+3x) dx 0

calculus
evaluate the definite integr 2 ∫ 5/(3+2x) dx 0

calculus help amigos
Find the point on the line 5x+5y+7=0 which is closest to the point (3,−4)

calculus help
integrate:dx/(3x^3-5)^3 i don,t know how to use wolframalpha plz show me step....

differential calculus
Beth leaves Muskegon, 30 mile north of Holland, traveling at 60 mph. Alvin leaves Holland traveling north at V=20t+40 mi/hr. When will Alvin pass Beth? How far from Holland will they be? :I think Beth's distance is d=60t-30 (using Holland as the frame of reference). Should I ...

integral calculus
help me integrate dx/(3x^3-5)^3 thanks

Calculus
Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of the function and the x-axis over the given interval. f(x) = x^2 + 4x, [0, 4]

Calculus
Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep safe. Since Dr. Jones is a mathematician, she suggests building fences described by y=4x^2 and x^2+10. Farmer Jones thinks this would be much harder than just building an enclosure...

Calculus
A bucket begins weighing 30 pounds, including the sand it holds. The bucket is to be lifted to the top of a 25 foot tall building by a rope of negligible weight. However, the bucket has a hole in it, and leaks 0.1 pounds of sand each foot it is lifted. Find the work done ...

calculus
calculus. suppose dR/dt= (d/R)^(2) and P(1) 4. separate the differential equation, integrate both sides

calculus help
integrate:dx/(3x^3-5)^3 help plz show step

calculus help
Integrate:(3x^5-5)^-3 dx thanks

calculus
find the derivative of d^2x/dt^2 if x^3=at^2 thanks

Pre calculus
Find the value for sin(theta), cos(2 theta)=3/4 and 270 degrees<0<360 degrees

calculus help me plz
integrate:dx/((x-1)sqrt(x^2-2) a tutor here direct me to a page but i do not know how to use it i tried but it did not show me any step...i need help plz

calculus plz help me
integrate:dx/((x-1)sqrt(x^2-2) plz show solution i plead

Calculus
approximate the change in the lateral surface area(excluding the area of the base of a right circular cone of fixed height of h=6m when its radius decreases from r=11m to r=10.9m S=(pi)r sqrt(r^2+h^2)

Math
Consider the distribution of mathematics SAT scores of students in honors calculus at a liberal arts college. What would you expect the shape and variation of the distribution to be? A. Symmetric with little variation B. Symmetric with large variation C. Skewed right with ...

Math
Consider the distribution of mathematics SAT scores of students in honors calculus at a liberal arts college. What would you expect the shape and variation of the distribution to be? A. Symmetric with little variation B. Symmetric with large variation C. Skewed right with ...

Math
Consider the distribution of mathematics SAT scores of students in honors calculus at a liberal arts college. What would you expect the shape and variation of the distribution to be? A. Symmetric with little variation B. Symmetric with large variation C. Skewed right with ...

Math
Consider the distribution of mathematics SAT scores of students in honors calculus at a liberal arts college. What would you expect the shape and variation of the distribution to be? A. Symmetric with little variation B. Symmetric with large variation C. Skewed right with ...

Calculus
Use Simpson's rule with n = 4 to approximate. Keep at least 2 decimal places accuracy. Integrate: (cos(x))/(x) x=1 to 5

Calculus
Use the trapezoidal rule with n = 5 to approximate. Keep at least 2 decimal places accuracy. Integrate: (cos(x))/(x) from x=1 to 5

Calculus 3
I need help writing the series 4 + 1/5 + .3 + 1/(3 + sqrt 2) + 1/(9+ sqrt 3) + 1/(27 + sqrt 4) + 1/(81 + sqrt 5 .... I have played with using irrational numbers, natural log and a vast variety of exponential arrangements. Any help to get me going in the right direction would ...

calculus
A hot air balloon is rising vertically upward from the ground. The crew of a boat from a nearby lake notices this situation and looks upward at an angle of 10 degree to see the balloon. If the boat is 400meters away from the balloon, and the angle of observation is changing at...

Calculus
Approximate the change in the lateral surface area(excluding the area of the base) of a right circular cone fixed height of h = 6m when its radius decreases from r=9m to r=8.9m (S=(pi)r sqrt(r^2+h^2)).

Pre-calculus
Consider an open-top box constructed from an 8.5 × 11 inch piece of paper by cutting out squares of equal size at the corners, then folding up the resulting flaps. Denote by x the side-length of each cut-out square. a) Draw a picture of this construction, and find a formula ...

calculus
rewrite each summation using the sigma notation. Do not evaluate the sums (a)3 + 4 + 5 + . . . + 93 + 94 (b)9 + 16 + 25 + 36 + . . . + 14

calculus
You own a small airplane that holds a maximum of 20 passengers. It costs you \$100 per flight from St. Thomas to St. Croix for gas and wages plus an additional \$6 per passenger for the extra gas required by the extra weight. The charge per passenger is \$30 each if 10 people ...

calculus
Find the dimensions of the rectangle with the largest area if the base must be on the x-axis and its other two corners are on the graph of: (a) y=16-x²,-4<=x<=4 (b)x²+y²=1 (c)|x|+|y|=1 (d)y=cos(x),-pi/2<=x<=pi/2

calculus
Evaluate lim (1³ +2³ +3³ +…+ n3)/n^4 n →∞ by showing that the limit is a particular definite integral and evaluating that definite integral.

calculus
Evaluate π ∫ tan² x/3 dx 0

calculus
Use the Fundamental Theorem of Calculus to find G'(x) if: G(x)=∫ up(x²) bottom(1) cost dt

calculus
Use the Fundamental Theorem of Calculus to find G'(x) if: /x² G(x)= / cos t dt / 1

calculus
I'm having trouble on this question: Find the area of the region in the first quadrant that is bounded above by the curve y= sq rt x and below by the x-axis and the line y=x -2.

Calculus
A conical cistern is 10 ft. across the top and 12 ft. deep. If water is poured into the cistern at the rate of 1 cubic foot per second, how fast is the surface rising when the water is 8 ft. deep?

Calculus
A particle travels along the parabola y=ax^2+x+b. At what point do its abscissa and ordinate change at the same rate?

Calculus
A light hangs 15 ft. directly above a straight walk on which a man 6 ft. tall is walking. How fast is the end of the man's shadow travelling when he is walking away from the light at a rate of 3 miles per hour?

calculus too hard help
if y=x^x^x^x... dy/dx=? plz show working thanks got no ideal at all

Calculus - urgent
A lamina. defined by y>=0 with edges y=0, y=3/2(1-x^2) and x=-y+2y^2, for which the density is given by p(x,y)=y. a) define domain as union of type 1 and type 2 region. b) Calculate mass of lamina.

calculus
Given the area is in the first quadrant bounded by y²=x, the line x=4 and the 0X What is the volume generated when this area is revolved about the 0X? the answer is 25.13 but I don't know how. help me please

Calculus
A cardioid r=1+cos(theta) A circle r=3*cos(theta) a) Define the domain of the region enclosed inside both the cardioid and the circle. b) Use polar coordinates to calculate the area. (We can use symmetry about x-axis)

Calculus
Air expands adiabatically in accordance with the law PV^1.4=Const. If at a given time the volume is 14 cubic feet and the pressure is 40 pounds per square inch, at what rate is the pressure changing when the volume is decreasing 1 cubic foot per second?

Calculus
One ship is sailing south at a rate of 5 knots, and another is sailing east at a rate of 10 knots. At 2 P.M. the second ship was at the place occupied by the first ship one hour before. At what time does the distance between the ships not changing?

Calculus
An island is 3 mi from the nearest point on a straight​ shoreline; that point is 6 mi from a power station​. A Utility company plans to lay electrical cable underwater from the island to the shore and then underground along the shore to the power station. Assume ...

Calculus
Optimization: A man on an island 16 miles north of a straight shoreline must reach a point 30 miles east of the closet point on the shore to the island. If he can row at a speed of 3 mph and jog at a speed of 5 mph, where should he land on the shore in order to reach his ...

calculus
Assume that the radius ,r , of a sphere is expanding at a rate of 10in./min. The volume of a sphere is V=43πr^3. Determine the rate at which the volume is changing with respect to time when r=5in. The volume is changing at a rate of how many in^3/min.?