# Homework Help: Math: Calculus

## Recent Homework Questions About Calculus

Differential Calculus
A water trough is 10 m long and a cross section has the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 80 cm wide at the top, and has height 50 cm. If trough is being filled with water at the rate of 0.2 m^3/min how fast is the water level rising when the ...

Calculus
Write the equation of the sphere in standard form. x2 + y2 + z2 + 4x − 2y − 2z = 19

calculus
Determine the points in the interval (0, 2π) at which the graph of the function below has a horizontal tangent line. f(x) = 10 cos x + 5 sin 2x There should be three

calculus
The graphs of f and g are shown. Let h(x) = f(g(x)) and s(x) = g(f(x)). f(-1)= 4 f'(x)=1 g(-1)=5 g'(-1)=-1/2 f(8)= 6 f'(x)= 2 g(x)= 2 g'(x)=-1/2 (a) Find h'(−1). (b) Find s'(8).

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
Find the vertical tangents of f(x)=10 cos x + 5 sin 2x

Calculus
Find, correct to the nearest degree, the three angles of the triangle with the given vertices. A(0, 1, 3), B(-2, 4, 5), C(1, 4, -3), ∠CAB = ° ∠ABC = ° ∠BCA = °

Calculus
State the domain and range of the function f(x) = 2sin(sqrt(3x-1)) + 3 Why is this so difficult?

Calculus
log base 4 of 8/log base 8 of 16 question is to simplify can you rewrite it this way? 4^x = 8 --------- 8^x = 16

Calculus
e^(1+2lnx) ----------- x^2 simplify

Calculus
If g(X) = 2+ln(x-5), find the inverse function, (g^(-1))(x) Solution: y = 2+ ln(x-5) e^y = 2 + x - 5 x = e^y + 3 y = e^x + 3 g^(-1) = y = e^x + 3 Is that right? I'm following an example - but don't really get it - how do I determine the domain and range - I know they flip when...

Calculus
Find the zero(es) of f(x) = (e^(7-2x)) - 1

math/Calculus
If h(x) = csc(x), find the inverse h^(-1)(x). express answer in terms of sin^(-1), cos^(-1) or tan^(-1) Don't know where to start -

Calculus
Hi, please I need help with this demonstration: If “f” , “g” :[ 0,1]→R are continuous functions, they are differentiable in (0,1), f(0)=0, g(0)=2 and │f ‘ (x)│≤1 ,│g ‘ (x)│≤1 for the interval (0,1). Prove that f(x) < g(x...

Calculus
Integral of (3^x)(e^x)dx

Calculus
Evaluate using tabular method: integral e^(2x)cos3xdx

calculus
find lim 1-2x / 1+6x x -> infinity find lim [ x / ((3+x)^2) -5] x -> infinity

Pre-calculus
Find the equation of the locus of the point which moves so that its distance from the point (2,0) is 2/3 its distance from the line y=5.

Pre-Calculus
Define the inverse secant function by restricting the domain of the secant function to the intervals (0, pi/2) and (pi/2, pi), and sketch the inverse function’s graph.

Pre-Calculus
Which of the following statements best describes the domain of the functions sine and arcsin? A)Sine domain is all real numbers; Arcsin domain is all real numbers. B)Sine domain is restricted; Arcsin domain is all real numbers. C)Sine domain is all real numbers; Arcsin domain ...

Calculus
a cone has an altitude of 12 cm and a base radius which increases at the rate of 3 cm per minute. When the radius is 6 cm,how fast is the vertex angle increasing?

calculus
find the area of the parallelogram that has vectors as adjacent sides u = -2i +j +5k v = 4i -3j -3k

calculus
find the triple scalar product u . (v * w) for the vectors u= (5, 9, -6) v= (5, 8, -1) w= (-2, 8, 3)

Pre-Calculus
Carmen rides her bicycle at a constant rate to the market. When she rides her bicycle back home along the same route, she bikes at three-quarters the rate she biked to the market. At any given time, t, the distance biked can be calculated using the formula d = rt, where d ...

Calculus
A statue 5m high is standing on a base 8m high. Is an observer's eye is 2.5 m above the ground, how far should he stand from the base of the statue in order that the angle between his lines of sight to the top and bottom of the statue be a maximum.

Calculus
If θ is an acute angle and tan(θ)=5/12, then sin(θ)=??

Calculus
Hello my problem is the next one: g is a function between the interval (a,b)and "p" is a fixed point in (a,b) that`s mean that g(p)=p. If g can be derivated in that interval and /g(x)/<1 to all the interval. Demonstrate using the Mean value theorem that there is ONLY one ...

calculus
find the inverse of the matrix. [ 16 1 ] 1 16

calculus
Find the product [ 3 8 ] [ 4 5 ] 6 3 4 4

calculus
Find A - B A = [ 3 7 8 ] 7 9 3 7 9 9 B = [ 2 2 6 ] 6 7 8 5 8 6

Pre-calculus
Plss... help me.. what is the equation of parabola with vertex on the line y=x, axis parallel to Ox, and passing through (6,-2) and (3,4)? thanks!

Calculus
A spherical balloon is inflated at the rate of 5 cubic feet/minute. What is the volume of the balloon if when the radius is increasing at the rate of 3 feet/minute?

calculus
Find all first and second partial derivatives of z with respect to x and y if x^2+4y^2+16z^2−64=0.

pre calculus honors
solve the system if possible | x+y+z = 15 | | < 7x+y+z = 75 | | | 3x+y-z=29 a. x=10,y=2,z=3 b. x=–10,y=–2,z=–3 c. x=3,y=10,z=–3 d. x=12,y=9,z=–3 e. no solution; inconsistent system

pre calculus honors
An object moving vertically is at the given heights at the specified times. Find the position equation s = 12 at^2 + v (small o) t + s (small o) for the object. At t = 1 second, s = 161 feet At t = 2 seconds, s = 98 feet At t = 3 seconds, s = 3 feet a. s=−8t^2−t&#...

Calculus
Solve the following equation on the interval [0,2pi) if sin = -0.29?

Calculus
Solve lim sin2x using any method. ×>0 ----- 5x I am unaware of what my first step is supposed to be, I know that if I plug in 0 to x, I will receive an answer of 0/0, and that makes my answer indeterminate. So what happens after that?

Calculus
Equal squares of side length x are removed from each corner of a 20 inch by 30 inch piece of cardboard, and the sides are turned up to form a box with no top. Write the volume V of the box as a function of x.

Calculus
A 100 inch piece of wire is cut into two pieces. Each piece of wire is used to make a square wire frame. Let x be the length of one piece of the wire. Determine an algebraic representation A(x) for the total area of the two squares.

calculus
Find lim as (x,y) goes to (0,0) of (e^(-x^2-y^2)-1)/(x^2+y^2).

Calculus
At what points c, if any, does lim x --> c f(x) exist? f(x) ={0, x < -1 {x, -1 ≤ x < 0 {1, x=0 {x, 0 < x ≤ 1 {0, x > 1

pre calculus work
given f(x)= 5x+4/5x^2+4x and g(x) = 1/x a. determine the domains of f(x) and g(x) b. simplify f(x) and find any vertical asymptotes c. explain how the two functions differ I have absolutely no idea how to answer this question - can you please help me to figure it out?!

calculus
A particle moves so that its position is given by ⟨cos(t),sin(t),cos(6t)⟩. Find the maximum and minimum speeds of the particle.

Pre Calculus
Two forces with magnitudes of 150 and 75 pounds act on an object at angles of 30° and 150°, respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer. Having lots of trouble with this...

Calculus
If F(x)=f(g(x)-h(x)), where g(3)=5, h(3)=4, g'(3)=3, h'(3)=1 and f'(1)=10, find F'(3). I know how to do derivatives and all, but I rlly can't figure this question out

Calculus
What are the zeroes of the polynomial equation, 𝑦 = 𝑥3 + 3𝑥2

Calculus
This question is killing me! :( Find the total area of the regions enclosed by the relations x=y^3-y+1 and x=-y^3-y^2+1. This is easiest if you integrate over y instead of x. Thank you so much in advance!

Calculus
Any help will be appreciated! Find the area of the region between x=-3pi/4 and 5pi/4 in the graph enclosed by f(x)=sinx and g(x)=cosx Thank you!

calculus
Find an equation of the plane containing the line of intersection of x+y+z=1 and x−y+2z=2, and perpendicular to the x-y plane.

Calculus
Hi, could you help me with this one please? Evaluate ∫sin(x)cos^2(x)dx by using the substitution u=sinx Ive done this by using u=cosx no problem but can't get this one :( Thank you so much in advance!

calculus
Do the three points (1,2,0), (−2,1,1), and (0,3,−1) form a right triangle? I think they do by using dot product. Do the three points (1,1,1)(1,1,1), (2,3,2)(2,3,2), and (5,0,−1)(5,0,−1) form a right triangle? I think they don't.

calculus
A force of 10 pounds is applied to a wagon, directed at an angle of 30∘30∘. Find the component of this force pulling the wagon straight up, and the component pulling it horizontally along the ground.

Pre-Calculus
Use a graphing utility to graph the function y = d + a sin (bx - c) for different values of a, b, c, and d. Write a paragraph describing the changes in the graph corresponding to changes in each constant.

Pre-Calculus
You are given the value of tan Θ. is it possible to find the value of sec Θ without finding the measure of Θ? Explain.

Calculus
The minute and hour hands on the face of a school clock are 8 inches and 6 inches long, respectively. Find the rate of change, in inches per minute, of the distance between the tips of the hands at 9:00.

Calculus
Find arccos (sqrt2/2). Can this be pi/4 and 7pi/4?

Calculus
Find dy/dx. e^(xy)=sin(x)

Calculus 1
Find the limit. lim x->0 (e^(6/x)+8x)^(x/2)

Calculus
Use L'Hoplital's rule to find the limit. Lim x->0 (3-3cos(x))/(sin(4x))

Calculus
The velocity of an object is given by the velocity function v(t)=t/42. If the object is at the origin at time t=0, find the position at time t=20.

calculus
Find the Maclaurin series of xcos(x^2).

Calculus with analytic geometry
What is the range and domain, x and y intercepts, symmetry and asymptote of this given equation, f(x) = 2x^2 - 8 / x-1

Math calculus
An ice cube is 3 by 3 by 3 inches is melting in such a way that the length of one of its side is decreasing at a rate of half an inch per minute. Find the rate at which its surface area is decreasing at the moment when the volume of the cube is 8 cubic inches

Given the following​ function, y=tan(pi-3x) 1)determine the interval for the principal cycle. (^ Type your answer in interval notation) 2)Then for the principal​ cycle, determine the equations of the vertical​ asymptotes 3)find the coordinates of the center&#...

Brief Calculus
The demand function for a certain brand of CD is given by p = −0.01x2 − 0.2x + 12 where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. The supply function is given by p = 0.01x^2 + 0.5x + 3 where p is the ...

Brief Calculus
The demand function for a certain make of replacement cartridges for a water purifier is given by the following equation where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. p = −0.01x2 − 0.3x + 10 ...

Calculus1
find the derivative using fundamental theorem of calculus integral of sin^3tdt from e^x to 0

calculus
Campbell’s Soup Company requires that is its tomato soup containers have a capacity of 64 in^3 , have the shape of a circular cylinder, and be made of aluminum. Determine the radius and height of the container that requires the least amount of metal.

calculus
Suppose that an arrow was fired vertically upward from a crossbow at ground level and that it struck the ground 20 seconds later. If air resistance may be neglected, find the initial velocity of the bolt and the maxim altitude that it reached.

Calculus
Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer. Between y = x^2 − 4x + 1 and y = −x^2 + 4x − 5 for x in [0, 3]

Calculus
What is the maximum area of a rectangle that has sides along the positive x-axis and y-axis and lies below the line 3x+2y=1

Calculus
Does the series converge? diverge? Use the Root test ((1/n)-(1/n^2))^n

Calculus
First make a substitution and then use integration by parts to evaluate. The integral of (x)(ln(x+3))dx What do you substitute first?

Calculus
Calculate the interval of convergence. Sigma from n=1 to infinity of (n!*x^n)/n^n. Calculus - Steve, Friday, July 29, 2016 at 11:52pm try using the ratio test. You should be able to show that the series converges for |x| < e I tried and I got |x|lim n-infinity of |(n/n+1)^n...

Calculus AB
A rectangle is inscribed in a right triangle with legs of length 5 and 12. The sides of the rectangle are parallel to the legs of he triangle. Find the dimensions of the rectangle that has the largest area?

Calculus AB
A 5.5 foot man walks away from a 12 fokt lampost at a constant speed. At a given moment, let l be the length of the man's shadow (along the ground) and ket x be his distance from the lampost. Sketch a figure that represents the problem Express l in terms of x

Calculus AB
The height h of a closed cylindical tank is 4 times longer than he radius r. Write the volume of the tank as a function of r. Write the total surface area of the tank in terms of h.

Calculus AB
Water pours at a constant rate into a conical tank of height 10 feet and radius 4 feet. Let V, h and r be the volume, height, and radius if the water in the tank at a particular time t. Express the volume of the water in the tank at any time t as a function of h only.

Calculus AB
Let f be the function that is given by f(x)=(ax+b)/(x^2 - c). It has the following properties: 1) The graph of f is symmetrical with respect to the y-axis 2) The graph of f has a vertical asymptote at x=2 3) The graph of f passes through the point (-1,3) Determine the values ...

Calculus AB
Theta is an angle between the lines L1 and L2 with the slopes m1 and m2. Prove that tan theta= (m2 - m1)/(1+m2m1).

Calculus AB
If r and s are roots of the pokynomial equation x^2 + bx + c, show that b=-(r+s) and c=rs

Calculus AB
Solve graphically (x-2)^3(x+4)(3-x)^2(x+1)^4 <0

Calculus AB
A hiker walks due east for 40 minutes, then changes course by going South 25 degrees West. After 20 minutes, he changes course again, this time at South 75 degrees East. He goes through this path for one hour after which he heads north reaching his final destination in 15 ...

Calculus AB
One of the equal angles of an isosceles triangle is 55 degrees. If the base is 20 cm, what is the perimeter and the area?

Calculus AB
From a height of 10 meters in the third floor of an apparent that building, the angle of depression of two cars moving on the same lane and in the same lane and in the same direction measure 29.5 degrees and 38.2 degrees. How far are the two cars from each other? This ...

Calculus AB
What is an algebraic expression for cot(arccos ((x+1)/2)?

Calculus AB
Without using a calculator, what is the exact value of sec(arctan(12/5)) - sin(arccot(3/4))

Calculus AB
The functions are f(x)= lnx, x>0 and g(x)=sinx. Let H be the composition of f with g, or H(x)=f(g(x)) and A) Find the domain of H B) Find the range of H C) Find the zeros of H

Calculus AB
If a sinusoidal function has a local maximum at (3,8) and the next local minimum at (7,-2), 1) What is the equation of a cosine function that has a graph characterized in the statement above 2) What is the equation of a sine function that has a graph characterized in the ...

Calculus
Calculate the interval of convergence. Sigma from n=1 to infinity of (n!*x^n)/n^n.

Calculus AB
If csc x = -2.5, what is the value of x?

Calculus AB
What are the six trigonometric functions of 2010 times pi?

Calculus AB
How do you solve a system of logarithmic equations? They have completely different bases: {(log(25)^3)x + (log(2)^7)y = log(5)^27 {(log(7)^8)x + (log(3)^5)y = log(49)^2

Calculus
divide 64 into two parts such that the product of one of them plus the cube of the other is a maximum

Calculus
If x^2 + y^2 = 25 and dx/dt = 8, find dy/dt when x=3.

Calculus - Differentials
The diameter of a shpere is measured to be 6 inches with a possible error of 0.05 inches. Use differentials to estimate the maximum error in the calculated surface area. I've gotten this far: A=4pir^2 dA=8(pi)(r)(dr) Since the problem gives me the diameter and the equation A=...

Calculus
A 20m ladder is leaning against a wall. Top of ladder is sliding down at 3m per second and the bottom is sliding away from the wall at 4m per second. How high is the top of the ladder and far is the bottom of the ladder from the wall.

Calculus
An open box is to be made from a rectangular piece of material by cutting equal squares of length x from each corner and turning up the sides. If the material is 18 inches long and 12 inches wide. What is the volume of the box as a function of x?

calculus
A farmer has 100 m of fencing to make a rectangular pen with 3 congruent rectangular subdivision side by side. Each subdivisions must be 3 meter wide and at least 8 meters long. What is the range of the possible length of it's division?

Calculus
Differentiate with respect to x 1/sin x

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