# Calculus

**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

**Calculus**

Sketch the regions bounded by the following curves and find their area: y=2x^2 y=-x^3+3x

**Calculus**

Assuming that Switzerland's population is growing exponentially at a continuous rate of 0.21 percent a year and that the 1988 population was 6.8 million, write an expression for the population as a function of time in years. (Let t=0t=0 in 1988.) I got 6.8 e^[0.021(t - 1988...

**Calculus**

Find the derivative of the function y=S 10(t)^1/2 sin(t)dt y'=? S=integration symbol b=x^3 a=(x)^1/2

**Calculus**

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=x^2,y=1; about y=7

**Math - Calculus**

a) Find the area of the region R bounded by the graphs of the equations y=2x−x^2, x=0, and y=0. b)The line y=cx, where c>0, divides R into two subregions. Compute the value of c for which the two subregions have the same area.

**Calculus**

The position at time t of an insect crawling along the x-axis is given by x(t) = t^3 - 3t^2 - 9t + 4. What is the maximum velocity on the closed interval 0 <= t <= 2?

**vector calculus**

Hi, I'm having trouble answering this question. The lines l1 and l2 are defined as l1: (x-1)/3 = (y-5)/2 = (z-12)/-2 l2: (x-1)/8 = (y-5)/11 = (z-12)/6 The plane j contains both l1 and l2. Find the Cartesian equation of j.

**Calculus**

Find the minimum value of the following function: h(x)= x-(12(x+1)^(1/3) -12) on the interval [0, 26] Honestly, I have found by graphing that the minimum value is at the coordinate point (9,-3), but I need to do this in a way that uses a more "calculus-like" method if you ...

**Calculus**

Hello, I'd appreciate any help with the following question below: Information: g(x)= 4 (x+1)^(-2/3) f(x)= ∫ g(t) dt The Question: What is f(26) ? (NOTE: I don't know how to do this on a key board, so I'll just say that while I did type an Indefinite integral for "f(x)" it is...

**Maths**

What is calculus ?

**Calculus**

Hello, I would greatly appreciate any help that I can have with the following calculus question below. It has to do with separable differential equations. I'm also going to explain what I've done so far, so please bear with me (but honestly I don't think I've done much). ...

**Calculus**

Consider the equation xy2 − x2y = 6. (a) Find all points on the graph when x = 2. (b) Find a formula for dy dx in terms of x and y. (c) Find the tangent lines for the points you found in the ﬁrst part

**calculus**

Find the exact length of the curve. x=(y^4)/8+1/(4y^2), 1 ≤ y ≤ 2.

**Calculus**

Sketch the region in the first quadrant enclosed by y=8/x, y=4x, and y=1/4x. Decide whether to integrate with respect to x or y. Then find the area of the region. Can someone please help me out with showing the work and not giving me some BS speech.

**Calculus**

Sketch the region in the first quadrant enclosed by y=8/x,y=4x and y=1/4x

**calculus**

Approximate the value of the series to within an error of at most 10^−5. The infinite series from n=1 to infinity (−1)^(n+1)/(n^6) according to the equation (2): |S_n - S| is less than or equal to a_(n+1) what is the smallest value of N that approximates S to within an ...

**Calculus indefinite integrals**

Evaluate the following indefinite integrals using substitution a) ∫ xsqrt(x^2-7) dx b) ∫ x^(2/3)(1/5x^(5/3)+2)^4 dx

**Calculus - Integrals**

Consider the region enclosed by the graphs of x=y^2-5 and x=3-y^2 a)Express the area of this region by setting up an integral with respect to x b) Express the area of this region by setting up an integral with respect to y c) Find the area of this region by evaluating one of ...

**Calculus**

Write the following function as the sum of an odd and an even function. Then calculate the integral over the given interval using the properties of odd and even functions. (x-1)^3, I=[-1,1]

**Calculus**

Find an equation of the curve that satisfies dy/dx=150yx^14 and whose y-intercept is 6.

**Calculus**

A particle is moving as given by the data below 4sin(t)-3cos(t); s(0)=0

**Calculus**

consider the function f(x) = 9/x^3 -10/x^7 let F(x) be the antiderivatice of f(x) with F(1)=) then F(x)=

**Calculus**

Consider the function f(x)= x^3+5 sqrt(x) Let F(x) be the antiderrivative of f(x) with F(10=-9

**Calculus**

Find the anti derivative for 4/(x^2+1)

**Calculus**

Apply the concepts of calculus (limits and derivatives) to describe the graph y = sec(x). Include a quality graph

**Calculus**

If y′= x(1+ y) and y > -1 , then y = The differential equation dy/dx=y/x^2 has a solution given by:

**Calculus**

If y′= x(1+ y) and y > -1 , then y = The differential equation dy/dx=y/x^2 has a solution given by:

**Calculus**

1. Can you identify holiday periods or special events that cause the spikes in the data? 2. What holiday results in the maximum sales for this department? 3. a) Generate linear and quadratic models for this data. b) What is the marginal sales for this department using each ...

**Calculus - Definite Integrals Please Help!**

h(x)=∫[-3,sin(x)] (cos(t^3)+t) dt

**Math - Calculus**

g(x)=∫[6x,3x] (u+2)/u-5) du Find g'(x)

**Calculus**

find f'(x)= f(x)=∫[1,x] t^t dt

**Calculus**

Find the derivative f'(x)= : f(x)=∫[2,x] ((1/2)t^2-1)^8 dt

**Calculus**

The velocity function is v(t)=t^2−5t+4 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-1,5]. So I found the antiderivative of the function, which gave me t^3/3-5^2/2+4x+c. Then plugging in the ...

**Calculus**

If f(x)=∫[3,x]t^5dt, then f'(x)= f'(-3)=

**Calculus**

Find all solutions to the equation with 0 is less then or equal to a is less then or equal to 2pi Give an exact answer if possible, otherwise give value(s) ofa accurate to at least four decimal places. 4tan(a)+5=2 a= how do i find a

**Calculus II: Finding the volume of a revolution**

Question: Find the volume of revolution bounded by y-axis, y=cos(x), and y=sin(x) about the horizontal axis. Since the rotation is happening at the horizontal axis, I thought the limits of integration would be [-1,1] and if the curves are rotated they would over lap so i used ...

**Calculus**

Find all solutions to tan(theta)=1/sqroot(3). In the interval 0 less then or equal to theta less then or equal to 2pi. Theta=

**Calculus**

If cos of theta= -7/12 and theta is in quadrant 2 then find a. tan(theta) cot (theta)= b. csc(theta) tan(theta)= c. sin^2(theta)+ cos^2(theta)=

**Calculus II: Shell Method for finding volumes**

Question: What is the volume of the revolution bounded by the curves of y=4-x^2 , y=x, and x=0 and is revolved about the vertical axis. First, I had found the points of intersection to get the limits and I got -2.5616 and 1.5616. And then I plug it in the shell method formula ...

**calculus**

The number of sunspots (solar storms on the sun) fluctuates with roughly 11-year cycles with a high of 120 and a low of 0 sunspots detected. A peak of 120 sunspots was detected in the year 2000. what is the trigonometric functions could be used to approximate this cycle?

**calculus**

the vertical displacement y of a boat that is rocking up and down a lake, with y measured relative to the bottom of the lake. It has a maximum displacement of 12 meters and a minimum of 8 meters, a period of 3 seconds and an initial displacement of 11 meter when measurements ...

**calculus**

suppose y'''=-6 y''(0)=2 y(1)=1 and y(2)=7 what is y ?

**Calculus**

After an hour of googling this as you suggested, I still can't find the discussions or proof you were referring to. Can you please either send the link you found or help me with this? I don't know how to even start it. Prove that the function defined by: f(x)={1 if x is ...

**calculus**

for trigonometric functions and rhythmic functions questions, how do you know when to use either f(t)=A sin (w(t-a)) or f(t) = A cos ( w(t-a)) ?

**Calculus**

Find the area of the region under the curve y=x+2 over the interval [1,4].

**calculus**

Evaluate ∫-3,3 x^z+2x+1dx using the definition of integration

**Calculus**

Prove that the function defined by: f(x)={1 if x is rational, 0 if x is irrational is not integrable on [0,1]. Show that no matter how small the norm of the partition, ||P||, the Riemann sum can be made to have value either 0 or 1.

**Math - Calculus**

Show that if f(x) is continuous and u(x) and v(x) are differentiable functions, then: d/dx ∫_v(x)^u(x) f(t)dt=u'(x)f(u(x))-v'(x)f(v(x))

**Calculus**

Find f if f''(x)=2+cos(x) f(0)=5 f(pi/2)=−3

**calculus**

Determine whether the integral is convergent or divergent.If it is convergent, evaluate it. from 0 to infinity e^(-y^1/2)dy

**calculus**

Determine whether the integral is convergent or divergent.If it is convergent, evaluate it. form -infinity to 0 x/(x^4+25)dx

**calculus**

Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. from -infinity to infinity 17xe^(-x^2)dx

**calculus**

Make a substitution to express the integrand as a rational function and then evaluate the integral. (Use C for the constant of integration.) 1/x{(x-1)^1/2} dx

**calculus**

Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) (11)/(x^3-125) dx

**Calculus**

Two planes leave an airport simultaneously. One travels north at 300 mph and the other travels west at 400 mph. How fast is the distance between them changing after 10 minutes?

**calculus**

Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) (x^2−x+12)/(x^3+3x) dx

**calculus**

y=-sin^2 (1/x) find the derivative

**Math calculus**

a cylindrical vat must hold 5m^3, the vat must be wider than it is tall, but no more than 3 m in diameter. What dimensions will use the least amount of material?

**Calculus**

Can someone explain to me why the derivative of sinx^2 is y'=2xcos (x^2)???

**Calculus**

Solve the following initial valued problems: a) g′(x) = sin(x), g(π) = 2. b) g′′(x) = 18x, g′(0) = 1 and g(0) = 5. b) g′′(x)=12x2 +2,g′(1)=7andg(1)=3.

**Calculus - Riemann Sum help**

How do I figure out the upper and lower bounds for a riemann sum? This question I'm working on tells me to assume: Δx=2π/n and x_i=iΔx and then gives me: n b lim ∑ sinx_iΔx = ∫f(x)dx n⟶∞ i=1 a Now I'm pretty sure f(x)=sinx, but I don't know how to find a or b. ...

**Math - Calculus**

Compute the sum: 81 ∑ (2i-1) i=1

**Calculus**

Find all solutions to the equation with 0≤α≤2π. Give an exact answer if possible, otherwise give value(s) of α accurate to at least four decimal places. 4tan(α)+5=2a=

**Calculus**

Using inverse trigonometric functions, find a solution to the equation cos(x)=0.2 in the interval 0â‰¤xâ‰¤4Ï€. Then, use a graph to find all other solutions to this equation in this interval. Enter your answers as a comma separated list. Thank you x=

**Calculus**

Solve the equations below exactly. Give your answers in radians, and find all possible values for t in the interval 0≤t≤2π. If there is more than one answer, enter your solutions in a comma separated list. (a) sin(t)=2/√2 when t= (b) cos(t)=1/2 when t= (c) tan(t)=−1 ...

**Calculus**

If tan(θ)=−7/2 and sin(θ)<0, then find (a) sin(θ)= (b) cos(θ)= (c) sec(θ)= (d) csc(θ)= (e) cot(θ)=

**Calculus**

If sin(θ)=8/10, 0≤θ≤π/2, then cos(theta)= tan(theta)= Sec(theta)= Please explain how to do this

**Calculus**

At the scene of an accident, there are skid marks which are 200 feet long showing where a car put on the brakes. The driver swears that he was obeying the speed limit. If we assume that the car braked with a constant deceleration of 16ft/sec^2. We can determine whether or not ...

**Math - Calculus**

Given f"(x)=5x+2 and f'(-3)=3 and f(-3)=-6 find f'(x)= find f(3)=

**Math (Calculus) Integrals**

Evaluate the integral using the following values. 8 ∫ x^3 dx = 1020 2 8 ∫ x dx = 30 2 8 ∫ dx = 6 2 2 ∫ x^3 dx = ? 2

**Calculus II**

I need to find if the summation of (n^4)/(n^10 + 1) is convergent or divergent from n=1 to infinity. I tried splitting it up into two sums, one being 1/n^6, which would be convergent because p=6>1, and then the other being n^4, but I'm not sure how to know if this is ...

**Calculus**

Determine if the Mean Value Theorem for Integrals applies to the function f(x) = x^3 − 16x on the interval [−1, 1]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem. f(a)=15 f(b)=-15 f'(x)=3x^2-16 f'(c)=-15 I am now lost from here, I do not ...

**urgent calculus help please**

A 20m long ladder is leaning against a wall. The top of the ladder is sliding down the wall at a constant speed of 2m/s. How quickly is the bottom of the ladder moving away from the wall when the bottom of the ladder is 5m from the wall? Give your answer as an exact expression.

**Calculus -math**

The Perfect Pizza Parlour estimates the average daily cost per pizza, in dollars, to be c(x)=0.00025x^2 +8x +10/x, where x is the number of pizzas made in a day. A) Determine the total cost at a production level of 50 pizzas a day B) Determine the production level that would ...

**Calculus**

Estimate the area under the graph of f(x)=cos((pi/4)x) from x=-2 to x=2 using 3 rectangles of equal width, using left and right endpoints.?

**calculus**

Find the derivative of (3x+17)^13 (14x+6)^11x^-4/5 / (20x +3)^-9 using logarithmic differentiation. Assume x > 0.

**Calculus**

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations y = 0.5x^2, y = 2, and x = 0 about the line y = 2. A. 8pi/15 B. 32pi/15 C. 64pi/15 D. 4pi/15 E. 16pi/15

**Calculus**

The region enclosed by the graph of y = x^2 , the line x = 2, and the x-axis is revolved abut the y-axis. The volume of the solid generated is: A. 8pi B. 32pi/5 C. 16pi/3 D. 4pi 5. 8pi/3 I solved for x as √y and set up this integral: 2pi * integral from 0 to 2 of y√y. But ...

**Calculus**

A manufacturer needs to produce a cylindrical can with a volume (capacity) of 1000cm cubed. The top and the bottom of the container are made of material that costs $0.05 per square cm, while the side of the container is made of material costing $0.03 per square centimeter. ...

**Math (Calculus II) (Graph approximation)**

Here is the link to the graph of f' in question: bit.ly/2oml70V I have a hard time trying to answer these kinds of questions when we're only given a graph of f'. a) Approximate the slope of f at x = 4. Explain. I believe the slope of f in this case would be a decreasing slope...

**Calculus**

A manufacturer needs to produce a cylindrical can with a volume (capacity) of 1000cm cubed. The top and the bottom of the container are made of material that costs $0.05 per square cm, while the side of the container is made of material costing $0.03 per square centimeter. ...

**calculus**

It is a dark clear night. The air temperature is 15◦ C. A body is discovered at midnight. Its temperature is 23◦ C. One hour later, the body has cooled to 20◦ C. Use Newton’s law of cooling to determine the time of death.

**calculus**

Evaluate the integral. from 0 to π/2 sin^3(θ)cos^5(θ) dθ

**Calculus**

Harold is in an airplane that is flying at a constant height of 4505 feet away from a fixed observation point. Maude, whose eyes are 5 feet from the ground, is standing at this point and watching the plane; the angle between her line of sight (the line line between her eyes ...

**Math - calculus**

Suppose f(x)=x^p where p>1 and [a,b]=[0,1]. According to the Mean Value Theorem there is at least one number c such that f(b)−f(a)=f′(c)(b−a). In this particular case the number c is unique but it depends on p. c=____ Your answer will be in terms of p.

**Calculus**

The point on the parabola y=x^2 that is closest to the point (2,1/2) is (___,___). The distance between the two points is _______.

**calculus**

The path of a baseball relative to the ground can be modelled by the function f(t)=−t^2+8t+1, where d(t) represents the height of the ball in metres, and t represents time in seconds. What is the speed of the ball when it hits the ground?

**calculus**

in your own words, describe how limits can be used to find the instantaneous rate of change of a function.

**calculus**

y' = 2y(1/2) , y(0) = 8 The function starts with y0 = 4 ,what is Euler’s method for computing yk+1 from yk with step size ∆t.

**calculus**

dy/dt = 2y^(1/2) y(0)= 2 What is Euler's method for computing yk+1 from yk with step size delta t when yo= 10

**calculus**

A farmer wants to construct a fence around a rectangular field. Sides with neighbours need reinforced fencing that costs $8 per meter. The other sides use regular fencing that costs $4 per meter. Assuming the farmer has neighbours on the east and west sides, answer the ...

**Pre-calculus**

An expedition walks 4 kilometers from camp on a bearing of 30 degrees, then turns and walks 10 km on a bearing of 160 degrees. Find the magnitude of the new location relative to the beginning location using vectors. -> if you can, can you possibly show how the triangle ...

**calculus**

x ln(3 + x) dx

**calculus**

Evaluate the integral. from 1 to 5 (ln(x))^2/x^3 dx.

**Calculus**

A box with a square base and no top is to be built with a volume of 6912 in^3. Find the dimensions of the box that requires the least amount of material. How much material is required at the minimum?

**Calculus**

For a cylinder with a surface area of 20 20, what is the maximum volume that it can have? Round your answer to the nearest 4 decimal places.

**Calculus**

A rectangular box has a square base. If the sum of the height and the perimeter of the square base is 14 in, what is the maximum possible volume?

**Calculus please help!**

The limit limh->0 ((sqrt1+h)-1)/h represents the derivative of some function f(x) at some number a. Find f and a. Please help!