# Homework Help: Math: Calculus

## Recent Homework Questions About Calculus

**Calculus**

let f(x)=2x-7. Use the rigorous definition of limit to show that lim x-->4 f(x)=1

**AP Calculus AB**

The function f is continuous on the interval [4, 15], with some of its values given in the table above. Estimate the average value of the function with a Right Rectangle Approximation, using the 4 intervals between those given points. x 4 9 11 14 15 f(x) -6 -11 -18 -21 -25 -11...

**Calculus**

lim x--> 2+ (tan(pi/x))

**Calculus**

Two positive numbers have the property that their product is 2 and their sum is as small as possible. Find their sum.

**Calculus**

Use pinching theorem to evaluate lim x-->1 ((x-1)sin(1/x-1)) I'm confused in the pinch theorem analytically

**Pre-Calculus**

Your computer supply store sells two types of laser printers. The first type, A, has a cost of $86 and you make a $45 profit on each one. The second type, B, has a cost of $130 and you make a $35 profit on each one. You expect to sell at least 100 laser printers this month and...

**Pre-Calculus Matrix**

Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. Show your work. 4x - y + 3z = 12 x + 4y + 6z = -32 5x + 3y + 9z = 20 4 -1 3 12 1 4 6 -32 5 3 9 20 I believe that the solution does not exist and how can I prove that?

**Pre-Calculus**

Solve the system of equations using matrices. Use Gaussian elimination with back-substitution. x + y + z = -5 x - y + 3z = -1 4x + y + z = -2 I really need help.. 1 1 1 -5 1 -1 3 -1 4 1 1 1 -2 I've done so many different methods to solve this and I get stuck..

**Pre-Calculus**

The Fiedler family has up to $130,000 to invest. They decide that they want to have at least $40,000 invested in stable bonds yielding 5.5% and that no more than $60,000 should be invested in more volatile bonds yielding 11%. How much should they invest in each type of bond to...

**pre-calculus**

A plane flies at a speed of 150mph at an angle of 10 degrees, after 6 seconds, the plane keeps the same speed but changes to an angle 18 degrees. How long in minutes would it take the plane to travel to a cruising altitude of 30,000 feet?

**maths-calculus help me**

differentiate Arccosh(x^2+1)*dy/dx if y=arcsinh(coth(x^2) plz showfull work i plead my brain is fried

**Calculus**

which of the following is equivalent to integral (a,b) k*f(x)+C)dx where k and C are constants k integral (a,b)(f(x)+C)dx ***** intergral (a,b)kdx + intergral (a,b)f(x)dx+ intergral (a,b) Cdx k integral (a,b)f(x)+ integral (a,b) Cdx integral (a,b) kdx * integral (a,b) f(x) dx...

**Calculus**

Find F'(x) for F(x)= integral[from 1 to x] of cos(t^3)dt

**Calculus**

lim (x--> infinidy) x^2/ln(x)= -1 0 1 e does not exist

**Calculus**

Which of the following grows faster than e^x as x--> infinity x^4 ln(x) e^-x 3^x .5e^x

**calculus**

Find the point on the line 4x+2y+5=0 which is closest to the point (-2,-1)

**Calculus**

Find the area bounded by the parabola 8+2y-y^2 and the lines y=-1 y=3

**Pre-Calculus**

Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. Show your work. 4x - y + 3z = 12 x + 4y + 6z = -32 5x + 3y + 9z = 20 Please help me..

**Pre-Calculus**

Solve the system by the substitution method. Show your work. 2y - x = 5 x2 + y2 - 25 = 0 I solved the problem but I got it wrong for some reason..can you solve it step by step?

**Pre-Calculus**

Locate the foci of the ellipse. Show your work. x^2/36+y^2/11=1 c^2=a^2-b^2 c^2=36-11 c^2=25 c= ± sqrt25 c= ±sqrt5*5 is this correct?

**Pre-Calculus**

Assume that x, y, and z are positive numbers. Use the properties of logarithms to write the expression 2lnx - 6lny + 1/3ln e^12 as a simplified logarithm. Is this 2lnx - 6lny + 4, or can it be simplified further?

**Pre-Calculus**

How do I find the domain of K(x) = x(32 - 2x)^2?

**Calculus**

A base of a solid is the region bounded by y=e^-x, the x axis, the y axis, and the line x=2. Each cross section perpendicular to the x-axis is a square Find the volume of the solid

**Pre-Calculus**

Find a polynomial with the zeros -1, 7, sqrt2, and -(sqrt2). Can this be f(x) = x^4 - 6x^3 - 9x^2 + 12x + 14?

**Pre-Calculus**

Find the vertical asymptotes, if any, of the graph of the rational function. Show your work. f(x) = (x-4)/(x(x-4)) (x-4)/x(x-4) the common factors cancel out and all is left is f(x)= 1/x... how do I solve this problem?

**Math (Calculus)**

Find the positive value of the parameter t corresponding to a point on the curve parametrized by {x= t^2 +3 ; y=t^2+t for which the tangent line passes through the origin. I tried with 2t+3 and 2t+1 but it isn't successful

**Math Calculus I**

let f(x)= 6sin(x)/(2sin(x)+6cos(x)) The equation of the tangent line to y= f(x) at a= pi/6 can be written in tthe form y=mx+b where m=? b=? I found the f': (9*(cos^2(x)+sin^2(x)))/(3cos(x)+sin(x))^2 but i don't know how to fill it into the form. Can anyone help me? ...

**Integral calculus**

find the area of the surface generated by revolving about x-axis the upper half of the ellipse 4x^2 + 16y^2 = 64

**Pre calculus**

olve the system of equations using matrices. Use Gaussian elimination with back-substitution. x + y + z = -5 x - y + 3z = -1 4x + y + z = -2 I need it explained to me, how do I do this?

**Calculus**

Two ships leave the same port at noon. Ship A sails north at 12 mph, and ship B sails east at 19 mph. How fast is the distance between them changing at 1 p.m.? (Round your answer to one decimal place.)

**Calculus**

Solve the differential equation: dy/dx = (3x^2) / (y+1) with initial conditions x = -1, y = 2 I have: ∫y + 1 dy = ∫3x^2 dx (y^2 / 2) + y = x^3 + C (2^2 / 2) + (2) = (-1^3) + C? 4 = -1 + C 5 = c (y^2 / 2) + y = x^3 + 5 Is this correct?

**Calculus**

Volume created when the area bounded by the curve y = 1/x, the x-axis, and the lines x = 1 and x = 4 is rotated about: a) the x-axis: 2.356 units^3 Is this correct? b) the line y = 5 I'm not sure how to do this one.

**Calculus**

when x intercept -3, point P(2,5,7) and Q(1,10,14) how to find x,y and z?

**MATH - CALC**

Use calculus and algebraic methods to do a complete analysis (i.e., intervals of increase and decrease, intercepts, critical points, points of inflection, and intervals of concavity) for each of the following functions and then sketch a graph of the function. (19 marks) ƒ(x...

**Calculus**

Solve the differential equation dy/dx = √[(x^3)(y)] with initial conditions x = 1, y = 2 so far i got y = (x^5)/25 + c so do i plug in 2 = (1^5)/25 + c 2 - (1/25) = c c = 49/25 = 1.96 is this correct?

**Calculus**

A particle with an initial velocity of -6 has its acceleration defined by a(t) = 2t+1. t is in seconds. find: a) its velocity equation b) the total distance traveled by the particle during its first 5 seconds of travel a) v(t) = t^2 + t - 6 b) 24.17 units is this correct?

**calculus-again frustrated-looking for steve asap**

if sinh(y)=[4sinh(x)-3)/(4+3sinh(x)] show that dy/dx=5/(4+3sinh(x)] step plz i plead

**calculus-help me sir~steve**

show that 2f''(t)-f'(t)-f(t)=sin(t)-cos(t) where f(0)=f'(0) has the solution (-2/5)e^(-t/2)-(1/5)sin(t)+(2/5)cos(t) using laplace tranformation plz plz plz show step by step

**Calculus**

Find the area of the region bounded by the curves y = x^(-1/2), y = x^(–2), y = 1, and y = 3. a) (1/2)(3)^1/2 + (4/3) b) 2*(3)^1/2 - (8/3) c) (1/2)(3)^1/2 - (32/3) d) 2*(3)^1/2 - (32/3) e) (8/3) - 2*(3)^1/2 So one thing that is throwing me off on this question is that I ...

**Calculus**

Design an Advanced U substitution problem whose answer must be exactly 6 and can be solved without using calculator?

**calculus-help.. .Me**

if y=e^(-kt)[Acosh(qt)+Bsinh(qt)] where A,B,q and k are constant show that d^2y/dt^2+2kdy/dt+(k^2-q^2)y=0 step plz thanks

**integral calculus**

A cylindrical tank of radius 3 ft length 8 ft is laid out horizontally .The tank is half full of oil that weighs 60 pounds per cubic foot. a.)determine the work done in pumping out oil to the top of the tank. b.)determine the work required to pump out the oil to leave 4 feet ...

**Calculus**

please solve it let f be the function defined over { 0 , ∞ ) as ∫ f(x) = x(ln(x)-1)^2 for x>0 and let (c) be its representative curve , we admit that f is continous at x=0 a ) determine lim f(x) / x as x approaching 0 b) find lim f(x) as x approaching infinity ...

**calculus**

Find the domain for the particular solution to the differential equation dy dx equals the quotient of 3 times y and x, with initial condition y(1) = 1.

**Calculus (Integration proving)**

Show that 0 <= [(integral)(integral, r to none)sin(pi)xcos(pi)y dA] <= 1/32 where R = [0,1/4]x[1/4]x[1,2]. Thank you.

**calculus**

If the graph of f " (x) is continuous and has a relative maximum at x = c, which of the following must be true? The graph of f has an x-intercept at x = c. The graph of f has an inflection point at x = c. The graph of f has a relative minimum at x = c None of the above is ...

**calculus**

R is the first quadrant region enclosed by the x-axis, the curve y = 2x + a, and the line x = a, where a > 0. Find the value of a so that the area of the region R is 18 square units.

**Pre-Calculus**

A drug is administered every 6 hours. The kidneys eliminate 55% of the drug over that period. The initial dose is 210 mg. Repeated dosage is 70 mg What is the “Difference equation”? Find the first seven terms of the of the solution sequence. Round to two digits each ...

**Pre-Calculus**

A drug is administered every 6 hours. The kidneys eliminate 55% of the drug over that period. The initial dose is 210 mg. Repeated dosage is 70 mg What is the “Difference equation”? Find the first seven terms of the of the solution sequence. Round to two digits each ...

**Calculus**

An observer 150 feet from point C, where a weather balloon has been released. The balloon rises vertically at a rate of 8ft/sec/. At the very instant the balloon is 250 above ground how far is it from the observer? How Quickly is it moving away from the observer at that moment...

**Calculus**

A car accelerates from rest at 1.1+2(t^1/2) m/h per second for 9 seconds find velocity after 9 seconds.

**calculus**

use logarithmic differentiation to find dy/dx for: [(x^2)(e^2)(x)] / [3√(2x-5)]

**Calculus**

Write a differential equation equivalent to "A chemical decomposition proceeds at a rate equal to the square of the amount of chemical present"

**Calculus**

find the particular solution of the differential equation that satisfies the conditions: f''(x)=sin(x)+e^(2x) f(0)=1/4, f'(0)=1/2

**Calculus**

solve the equation y'=(sqrt(x))/2y

**Calculus**

given d/dx[f(2x)]=f'(x) and f'(1)=1 find f'(2) the choices are 1/4, 1/2, 3/4, 3/2, or 5/2 if it helpes

**Calculus**

Find the particular solution of differential equations that satisfies the initial condition dx/dy=e^(x+y) x(1)=0 I know you have to get all the y and dy on one side and x and dx on the other so you can intagrate and stuff, but im having trouble getting there

**Differential Calculus**

From a faucet, a constant inflow of water is to fill a conical vessel 15 feet deep and 7.5 feet in diameter at the top. water is rising at the rate of 2 feet per minute when the water is 4 feet deep. what is the rate of inflow in ft^3/min?

**Calculus**

Inflection point of 3y=x^3+3x^2-9x+3

**Calculus**

I need help I have to submit work at 12 est time

**Calculus**

Need help with a few questions

**integral calculus**

Find the area between the curves y=5x and 2y=5x^2

**Calculus question ?**

Are there any horizontal asymptote on a ln natural log function

**Grade 12 Calculus and Vectors**

A homeowner wants to enclose a rectangular garden with fencing The garden will be adjacent to his neighbours lot. There will be fencing on all four sides. His neighbour will be paying for half of the shared fence. What should the dimensions of the garden be if the area is 432 ...

**Pre-Calculus**

Determine the magnitude of the positive vectors from the origin to to the following points. A. (3,4) B. (12,5) C. (3,-2) D. (-7,-3)

**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