# Calculus

**calculus**

A rotating light is located 25 feet from a wall. The light projected on the wall is moving at a rate of 1.5 feet per second when the light's angle is 15 degrees from perpendicular to the wall. If the light is turning at a constant rate, how many seconds does it take to go ...

**Calculus**

A rotating light is located 25 feet from a wall. The light projected on the wall is moving at a rate of 1.5 feet per second when the light's angle is 15 degrees from perpendicular to the wall. If the light is turning at a constant rate, how many seconds does it take to go ...

**Math (Calculus II) (Weird Work Problem Setup Help)**

I am trying to understand my teacher's example of a Work problem. Cut to the chase here's a picture of the problem: goo.gl/photos/AqZ6ENmHLg6heixD7 While I understand how to integrate fairly well, I'm still confused on how exactly my teacher set up the work problem. Since work...

**multivariate calculus**

Q.NO.1: Show that the function z=ln(x^2 + y^2)+2tan^-1(y/x) satisfies Laplace’s equation. (∂^2z/∂x^2)+(∂^2z/∂y^2)=0

**Calculus**

Find the limit. lim 1/x^2-4 a)x->2^+ b)x->2^- c)x->-2^+ d)x->-2^- I'm completely lost. I don't understand how some answers are infinity and the others are negative infinity.

**Calculus Please Check my answer**

The rate at which water flows into a tank, in gallons per hour, is given by a differentiable function R of time t. The table below gives the rate as measured at various times in an 8-hour time period. t---------0-----2------3-------7----8 (hours) R(t)--1.95---2.5---2.8----4.00...

**Calculus**

f is a continuous function with a domain [−3, 9] such that f of x equals 3 for x between negative 3 and 0 including negative 3, equals negative 1 times x plus 3 for x between 0 and 6 inclusive, and equals negative 3 for x greater than 6 and less than or equal to 9 and let g ...

**calculus**

Q.NO.4: Find the arc length of the graph of r(t). r(t)=(t^2)i +(cost + t sint)j +(sint- t cost)k , 0≤t≤π

**calculus**

Q.NO.3: Show that the function z=tan^-1(2xy/x^2-y^2)satisfies Laplace’s equation; then make the substitution x=r cosθ, y= r sinθ and show that the resulting function of satisfies the polar form of laplace’s equation (∂^2z/∂r^2)+(1/r^2)(∂^2z/∂θ^2)+(1/r...

**calculus**

Q.N0.2: Show that u(x,y)=ln(x^2 + y^2) and v(x,y)=2tan^-1(y/x) satisfy Cauchy-Riemann equations (∂u/∂x)=(∂v/∂y) and (∂u/∂y)=(-∂v/∂x)

**calculus**

Q.NO.1: Show that the function z=ln(x^2 + y^2)+2tan^-1(y/x) satisfies Laplace’s equation. (∂^2z/∂x^2)+(∂^2z/∂y^2)=0

**PLEASE HELP BEEN STUCK ALL DAY CALCULUS**

Using 4 equal-width intervals, show that the trapezoidal rule is the average of the upper and lower sum estimates for the integral from 0 to 4 of x squared, dx.

**calculus**

Elasticity a) Find the elasticity of the demand function q + 2p = 5000 when p = $1000, and q = 3000. b) How would revenue be affected by a price increase?

**Calculus I'm really confused**

solve the differential equation dy/dx=y^2/x^3 for y=f(x) with condition y(1)=1.

**Calculus Please Check my answer**

The table below gives selected values for the function f(x). Use a trapezoidal estimation, with 6 trapezoids to approximate the value of integral from 1 to 2 f(x) dx =.1*4/2+.1*7/2+.3*10/2+.2*13/2+.2(15/2)+.1*18/2 =4.40

**Calculus**

The slope of the tangent to a curve at any point (x, y) on the curve is -x/y . Find the equation of the curve if the point (3,-4) on the curve.

**Calculus**

Suppose an airline policy states that all the baggage must be boxed shaped with a sum of length, width, and height not exceeding 138 inches. What are the dimensions and volume of a square based box with the greatest volume under these conditions.

**Calculus**

A light in a lighthouse 5 kilometers offshore from a straight shoreline is rotating at 4 revolutions per minute. How fast is the beam moving along the shoreline when it passes the point 5 kilometers from the point opposite the lighthouse?

**calculus**

Find the area of the region enclosed by the parametric equation x = t^3−3t y = 6t^2.

**calculus**

Notice that the curve given by the parametric equations x=25−t^2 y=t^3−16t is symmetric about the x-axis. (If t gives us the point (x,y),then −t will give (x,−y)). At which x value is the tangent to this curve horizontal? x = ? At which t value is the tangent to this ...

**calculus**

Find the length of the curve deﬁned by the parametric equations x = 2/3t, y = 2ln((t/3)^2−1) from t =6 to t =7.

**Calculus**

A rectangular page is to contain 8 square inches of print. The margins at the top and bottom of the page are to be 2 inches wide. The margins on each side are to be 1 inch wide. Find the dimensions of the page that will minimize the amount of paper used. (Let x represent the ...

**Calculus**

At what point is the function y=csc(2x) continuous?

**calculus**

from a cardboard box 12 in by 8 inches are cut out so the sides can be folded up to make a box . What dimentions will yield a maximum volume? What is maximum volume? we got our V = 4x^3--40x^2+96x V'=12x^2-80x +96 then we know to use quadratic equation I get 20( +/-) sqrt 112/...

**calculus**

If x = 18cos^3θ and y = 18sin^3θ, ﬁnd the total length of the curve swept out by the point (x,y) as θ ranges from 0 to 2π.

**calculus**

Consider the curve deﬁned by the equation y = 4x^3 +3x. Set up an integral that represents the length of curve from the point (0,0) to the point (4,268).

**Calculus**

Compute the absolute and relative errors in using x to approximate x. x=pi; c=3.18

**Calculus**

Consider the differential equation dy/dx = 2x - y. Let y = f(x) be the particular solution to the differential equation with the initial condition f(2) = 3. Does f have a relative min, relative max, or neither at x = 2? Since we're trying to find a max/min I don't think it's ...

**Calculus**

If lim x->4 f(x)-5/x-2 =1, find lim x->4 f(x). I know the answer is 7, I need help on solving it. Thanks

**Pre-calculus**

Can someone help me with this equation: y = (2*10^(-44))*(e^(0.055x))?

**calculus**

Hi, I have the following HW question and I'm a little confused: Find the volume of the solid generated by revolving the region bounded by y=1/sqrt(x) and y=0 for 1 <= x <= 2 about the line y=-1. So far I have the integral 2pi (-1-y)(1-1/y^2) dy from -1 to 1, but that's ...

**calculus**

Find the area of the shaded region. r^2=sin(2θ).

**calculus**

Find the slope of the tangent line to the given polar curve at the point specified by the value of θ. r=6/θ, θ=π

**calculus**

Find a Cartesian equation for the curve and identify it. (r^2)cos(2θ)=1

**calculus**

Find the exact area of the surface obtained by rotating the given curve about the x-axis. x=t^3, y=t^2, 0 ≤ t ≤ 1

**calculus**

Find the area enclosed by the curve x = (t^2)-2t, y = (t)^(1/2) and the y-axis.

**Calculus**

I am given the true of false question: If f(x) is continuous and 0<=f(x)<=1 for all x in the interval [0,1], then for some number x f(x)=x. This seems intuitively true, but I'm not sure. All help is greatly appreciated.

**Calculus**

A particle's position along the x-axis is given by x(t) = t^4/24 - t^3/2 + 2t^2 - 1. What is the maximum acceleration on the interval 0 <= t <= 4? I found the acceleration to be (t^2 - 6t + 8)/2 and the derivative of the acceleration to be t - 3. I thought the maximum ...

**Calculus**

A differentiable function called f(x) achieves its maximum when x=0. Which of the following must then be true? 1. The function p(x) = xf(x) has a critical point when x = 0. 2. The function m(x) = (f(x))^2 has its maximum at x = 0. 3. The function j(x) = f(x^2) has its maximum ...

**Calculus**

Let the length of a rod be 10 meters and the linear density of the rod ρ(x) be written in the form ρ(x) = ax + b with x = 0 representing the left end of the rod and x = 10 representing the right end of the rod. If the density of the rod is 2kg/m at the left end and 17 kg/m ...

**calculus**

Hi, could someone please help me with this hw question asap? Given that the integral of (e^x*sin(5x))dx=((e^x)/26)*(sin(5x)-5cos(5x))+c, evaluate the integral from 1 to e^(pi/10) of sin(5ln(x))dx

**calculus**

Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x=tcos(t), y=tsin(t); t=π

**calculus**

x = sin(θ/2), y= cos(θ/2), −π ≤ θ ≤ π. Eliminate the parameter to find a Cartesian equation of the curve.

**Calculus**

Use cylindrical shells to find the volume formed by rotating the region in the first quadrant enclosed by: y=1.2-1.4|x-12| and y=0 about the y-axis

**Statistics**

In how many different ways can a chemistry book, a calculus book, a history book and a dictionary be arranged on a shelf so that the chemistry book or the history book appears first?

**Calculus**

Use cylindrical shells to find the volume formed by rotating the region in the first quadrant enclosed by: y=1.2-1.4|x-12| and y=0 about the y-axis

**Calculus**

Use washers to find the volume formed by rotating the region enclosed by: y=1.4−2|x−13| and y=0 about the y-axis

**Calculus I**

A particle on the x-axis is moving to the right at 2 units per second. A second particle is moving down the y-axis at the rate of 3 units per second. At a certain instant the first particle is at the point (5,0) and the second is at the point (0,7). How rapidly is the angle ...

**Calculus Please Check my answer**

An object has a constant acceleration of 30 ft/sec2, an initial velocity of −10 ft/sec, and an initial position of 4 ft. Find the position function, s(t), describing the motion of the object. s(t)=4-10t+15^2

**Calculus Please Check my answer**

Set up, but do not evaluate, the integral which gives the volume when the region bounded by the curves y = Ln(x), y = 1, and x = 1 is revolved around the line y = -1. ANSWER: v = ∫[1,e] π(4-(lnx+1)^2) dx

**Calculus**

Find the area of the region bounded by the curves of y=sin^-1(x/4), y=0, and x=4 obtained by integrating with respect to y. Your work must include the definite integral and the anti-derivative. I am really confused on this question. I graphed all of the points, but I have no ...

**Calculus**

Determine if the Mean Value Theorem for Integrals applies to the function f(x) = x^3 - 9x on the interval [-1, 1]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem. I think one point is zero.

**Calculus**

The base of a solid in the xy-plane is the first-quadrant region bounded y = x and y = x^2. Cross sections of the solid perpendicular to the x-axis are equilateral triangles. What is the volume, in cubic units, of the solid? So I got 1/30 because (integral from 0 to 1) (x-x^2...

**Math (Calculus) (Work)**

Six and one-half foot-pounds of work is required to compress a spring 4 inches from its natural length. Find the work required to compress the spring an additional one-half inch. (Round your answer to two decimal places.) This is what I did so far: 4 in = 1/3 ft 6.5 = ∫[0,1/...

**ASL**

1. Nodding your head should be added to which statement or question? (1 point) Who is your brother? Recently, I took an American Sign Language course. Yes, I agree. No, I don’t think so. 2. Shaking your head should be added to which statement or question? (1 point) Who is ...

**Calculus**

Which of the following integrals will find the volume of the solid that is formed when the region bounded by the graphs of y = ex, x = 1, and y = 1 is revolved around the line y = -2

**Calculus**

For an object whose velocity in ft/sec is given by v(t) = −2t^2 + 4, what is its distance travelled, in feet, on the interval t = 0 to t = 2 secs? I think the answer is 2.667 but I am not one hundred percent sure.

**Calculus**

find the area of the region bounded by the graphs of y=x^2 and y=cos(x)

**Calculus**

find the area of the region bounded by the graphs of y=-x^2+5x+2 and y=2

**calculus**

Let y = sinx + ztanx,where z is a function of x. If (dy/dx)= z+ cosx, show that (d^2y/dx^2) =-y. I really have no idea how to do this. Please show me

**Calculus**

Find the distance traveled by a particle with position (x, y) as t varies in the given time interval. x = cos^2 t, y = cos t, 0 ≤ t ≤ 9π and the length of the curve so far i got ∫0 to 9pi √((-2cos(t)sin(t))^2+(-sint)^2) I am having trouble integrating from here

**Calculus**

Determine the remainder for Sn where n=5 or n=9 for the following series. ∑n=1 to ∞ (n^2+1)/(n^4) S5= R5= S9= R9=

**Calculus**

find the volume of the solid formed by revolving the region bounded by the graphs of y=x^3 y=1 x=2 about the y-axis

**Calculus**

The temperature of a pan of hot water varies according to Newton's Law of Cooling: dT dt equals negative k times the quantity T minus A, where T is the water temperature, A is the room temperature, and k is a positive constant. If the water cools from 90Â°C to 85Â°C in 1 ...

**Calculus**

The slope of the tangent line to a curve at any point (x, y) on the curve is x divided by y. What is the equation of the curve if (2, 1) is a point on the curve?

**Math (Calculus II) (Volume Revolution Setup)**

Consider the graph of y^2 = x(4-x)^2 (see link). Find the volumes of the solids that are generated when the loop of this graph is revolved about (a) the x-axis, (b) the y-axis, and (c) the line x = 4. goo.gl/photos/v5qJLDztqsZpHR9d7 I'm just having trouble trying to set up the...

**Calculus**

Find the first 5 partial sums of the series ∑n=2 to ∞ 1/(n(n+4))? I got 1/12 for the first one but when I put 1/21 for the next one it says it's wrong please help

**Calculus**

The divergence test applied to the series ∑n=1 to ∞ 3n/(8n+9) tells us that the series converges or diverges? I got that it was divergent because it was undefined at infinity, is my answer right?

**calculus**

The differential equation below models the temperature of a 87°C cup of coffee in a 17°C room, where it is known that the coffee cools at a rate of 1°C per minute when its temperature is 67°C. Solve the differential equation to find an expression for the temperature of the...

**Calculus Help Please**

Hello! I am struggling with this problem: Find the Taylor Series for sin(x-2) centered at c=3. My work so far: sin(1)+(x-3)cos(1)-(1/2)(x-3)^2sin(1)-(1/6)(x-3)^3cos(1)+(1/24)(x-3)^4sin(1)... I know that the Taylor series for sign is typically: the summation from n=0 to ...

**calculus help please!**

Water is poured into a bucket according to the rate F(t)=(t+7)/(t+2) , and at the same time empties out through a hole in the bottom at the rate E(t)=(ln(t+4))/t+2 , with both F(t) and E(t) measured in pints per minute. How much water, to the nearest pint, is in the bucket at ...

**Calculus**

Find the area of the region bounded by y = x^2, y = 0, x = -1, and x = 2. I tried the integral from -1 to 2 of x^2 and got 3 as the answer. I tried (integral from 0 to 1 of √y + 1) + (integral from 0 to 4 of 2 - √y) and got 13/3. What is wrong with the way the integrals ...

**calculus review please help!!**

The velocity of a particle moving along the x-axis is v(t) = t^2 + 2t + 1, with t measured in minutes and v(t) measured in feet per minute. To the nearest foot find the total distance traveled by the particle from t = 0 to t = 2 minutes.

**Pre-Calculus**

Annual sales of fountain pens in Littleville are 2,000 per year and are increasing by 10% per year. How many fountain pens will be sold over the next five years? Use an integral to solve this problem. I just need help setting the problem up - thank you!

**Calculus**

S(12x+6)(3x^2+3x+5)^7 S=integral sign please help I am stuck :(

**Calculus**

The radius of a circle is increasing at a rate of 3 ft/min. If the radius is 0 when the time is 0, how fast is the circle's area changing when time is at 10 minutes?

**Math - Calculus**

Suppose you live near a bay where the water level fluctuates due to the tides. Your bay is an inverted cone with a radius of 1 mile, and a depth in the center of 100 feet. (There are 5280 feet in a mile.) Water flows through a channel in and out of the bay with the tides. You ...

**Math(Calculus)**

Im having a real difficult time solving this question. Find the absolute extrema of the function. h(x) = e^x^(2) - 4 on [-2,2] Absolute maximum value: at x = Absolute minimum value: at x =

**Calculus**

Use the disk method to find the volume of the solid generated by revolving about the y-axis the region bounded by the curves y=8−x^2 and the curve y=x^2.

**Calculus - Fundamental thm of Calc**

Use the Fundamental Theorem of Calculus to find the derivative of f(x)=∫[4,x^2]((1/4)t^2−1)^15 dt

**Calculus - Related Rates**

A road perpendicular to a highway leads to a farmhouse located 5 miles away. An automobile traveling on the highway passes through this intersection at a speed of 65mph. How fast is the distance between the automobile and the farmhouse increasing when the automobile is 1 miles...

**Calculus Help**

Suppose you drill a circular hole with radius r through the center of a sphere with radius R. You remove exactly half the volume of the sphere. The ratio of your radii is: r/R=

**calculus please help!!**

Find the range of the function F(x)= definite integral from [-6,x] of sqrt(36-t^2)dt. [0, 36π] [0, 18π]*** [-6, 6] [-6, 0]

**Pre calculus**

write the finite series -1+2+7+14+23+...+62 in summation notation

**Pre calculus**

When “superballs” sprang upon the scene in the 1960’s, kids across the United States were amazed that these hard rubber balls could bounce to 90% of the height from which they were dropped. If a superball is dropped from a height of 2 m, how far does it travel by the ...

**Calculus**

The function f is continuous on the closed interval [-5,5], and f(-2) = 6, f(1) = -3, and f(4) = 6. Which of the following statements must be true? A. The equation f(x) = 0 has at least two solutions on the closed interval [-5,5]. B. The equation f(x) = 0 has exactly two ...

**calculus**

find the parametric equation of the line that is tangent to the parabola y=x^2 at the point(-2 , 4)

**Calculus**

If dy/dt = k/y and k is a nonzero constant, which of the following could be y? A. y = √(2kt + 16) B. y = kt + 5 C. y = √(kt + 16) D. y = 5e^(kt) E. y = √(2kt) + 4 I got E by finding the integral of y dy = k dt.

**calculus**

Find the exact area of the surface obtained by rotating the curve about the x-axis. y=((x^3)/4)+(1/3X), 1/2≤X≤1

**Calculus (trig derivatives)**

A lighthouse 2 miles offshore has a light that rotates once every 20 seconds. At what rate is the light traveling along the shore if it is shining on a point 4 miles along the shore from the point nearest the lighthouse?

**Calculus**

If g(x) = integral from 0 to x^2 of √(t^3+2) then g'(2) = ?

**Calculus**

If y = 18 - 3x, what is the maximum value of the product 2xy? A. -3 B. 0 C. 3 D. 6 E. 54 I found that the value of the maximum occurs at x = 3, but that the value itself is 54. Is E the answer?

**calculus**

In this problem, you will investigate the error in the nth degree Taylor approximation to ln(x+1) about 0 for various values of n. (a)Let E_1=ln(x+1)−P_1(x)=ln(x+1)−(x). Using a calculator or computer, graph E1 for −0.1≤x≤0.1, and notice what shape the graph is. Then...

**Calculus PLSSSSS HELP DUE SOON**

Assuming P≥0, suppose that a population develops according to the logistic equation dP/dt=0.03P−0.00015P^2 where tt is measured in weeks. Answer the following questions. 1. What is the carrying capacity? I tried solving the differential equation and got 600 but it says it'...

**Calculus 1 Help**

Find the volume generated by rotating about the given line a) y^2=x, x=2y; about the y-axis b) y=x, y=sqrtx; about y=1

**Calculus Math**

Find the height of y=((sqrtx)(3-x))/3 for 0<=x<=3 Use the arc length formula and note that 1/4x+1/2+x/4=(1/(2sqrtx) + sqrtx/x)^2 is a perfect suare.

**Calculus Help**

A solid generated by rotating about the x-axis the region under the curve of f(x) from x=0 to x=b, is b^2 FOR ALL b>0. Find the function f.

**Math - Calculus**

Find the volume of the solid given by rotating the region bounded by the curves y=x^2, x=1, x=2, and y=0 around the y-axis a) Use the shell method b) Use the washer method. Be careful with the radius of the washer at different y.

**calculus please help!!**

b. Explain why the initial value problem y'=4xsqrt(1-y^2) with y(0) = 4 does not have a solution. I already solved the differential equation and got y=sin(2x^2+C) I don't know what to do from there

**calculus**

3) The table below gives selected values for the function f(x). Use a trapezoidal estimation, with 6 trapezoids to approximate the value of int f(x) dx from 1 to 2 . Give 3 decimal places for your answer. x 1 1.1 1.2 1.5 1.7 1.9 2.0 f(x) 1 2 4 6 7 9 10