# 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

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

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