# Calculus

Calculus
What is the best substitution to make to evaluate the integral of the quotient of cosine of 2 times x and the square root of the quantity 5 minus 2 times the sine of 2 times x, dx? u = sin(2x) u = cos(2x) u = 2x u = 5 − 2sin(2x)

calculus help pls
What is the best substitution to make to evaluate the integral of the quotient of cosine of 2 times x and the square root of the quantity 5 minus 2 times the sine of 2 times x, dx? These are the choices: u = sin(2x) u = cos(2x) u = 2x u = 5 − 2sin(2x)

Pre-Calculus 12
how to solve 3^(x-2) = 5^x

Calculus
The shoreline of a lake is a circle with diameter 3 km. Peter stands at point E and wants to reach the diametrically opposite point W. He intends to jog along the north shore to a point P and then swim the straight line distance to W. If he swims at a rate of 3 km/h and jogs ...

Math/Pre-calculus
Assume that the number of bacteria follows an exponential growth model: P(t)=P0e^k/t. The count in the bacteria culture was 400 after 10 minutes and 1500 after 35 minutes. (a) What was the initial size of the culture? (b) Find the population after 85 minutes. (c) How many ...

pre-calculus
x^2+6x+8y=7 Find the: Direction: Vertex: Focus: Axis of Symmetry: Directrix:

Calculus
Find the limit x->pi/2^+ tan(x) I know the answer is -∞, but I don't understand why. When I simplify to sin(x)/cos(x), I get 1/0^+.

Multivariable calculus
I have to show that the relative error of the product of two positive numbers is aproximately to the sum of the relative errors of its factors. My teacher told me to use first order approximation, but I don't know how to use it.Please help

Calculus
two sides of a triangle have lengths 15 m and 20 m. the angle between them is increasing at a rate of pi/90 rad/s. At what rate is the area changing when the angle between the two given sides is pi/3 Can't seem to figure it out!

Calculus
Hi, I have this question here that I'm not sure about. Any help is appreciated. Evaluate the integral from 1 to 3 of dx/(x-2). This seems like it should be really simple- is it 0?

Calculus
S=integral sign S3x(4-x^2)^1/2 use trig substitution I am confused I got x sin(sin^-1(x/2))+cos(sin^-1(x/2))

Calculus
(1,1)(2,1)(2,3) mirror Revolve around y-axis. solve with Shell and washer please and thank you! Made a correction for washer would R(x)=2x-1 ? what about r(x)

Calculus
(1,1)(2,1)(2,3) mirror around y-axis & revolve solve with Shell and washer please and thank you

Multivariable calculus
Hello, I have the next exercise about chain rule in multivariable calculus: I have to show that the differential equation: y(dz/dx)-x(dz/dy) = (y-x)z can be change to the equation: (dw/dv) = 0 using the new variables: u= (x^2)+(y^2) v = (1/x)+(1/y) w = ln(z)-(x+y) For that I ...

Calculus
the region D is the triangle with vertices (1,1) (3,1) (3,2) about the y-axis find r(x) and h(x) using the shell method. My teacher got r(x)=x and h(x)=(1/2x+1/2)-1 but how did he get the equation for h(x)??

Pre-Calculus
a ferris wheel is elevated 1 meter above ground. When car reaches the highest point of the Ferris wheel, it's altitude from ground level is 31 metres. How far away from the center, horizontally, is the car when it is at an altitude of 25 meters?

Pre-Calculus 12
I am refering to the question posted on Tuesday, June 6, 2017 at 8:26pm. "how to graph y= (x^2-3x-10)/(x-2)" This is the reply I got: Pre-Calculus 12 - Damon, Tuesday, June 6, 2017 at 9:21pm (x-5)(x+2)/(x-2) well we know it is 0 at x = 5 and at x = -2 and we know it explodes ...

Calculus
if a penny is dropped from the top of a 320 ft. building, how fast will it be moving when it hits the ground? So we can find the speed of the penny as instantaneous rate of change of height of penny when it hits ground. Instantaneous rate of change of y with respect to x is dy...

Calculus
if a penny is dropped from the top of a 320 ft. building, how fast will it be moving when it hits the ground? v2 = u2 + 2gH, Here, u = initial velocity = 0 v = final velocity g = 32ft/s2 H= 320ft So, v2= 0 + 2 × 32 × 320 or,. v = ✓(2×32×32×2×5) or, v = 64✓5 ft/s is ...

Pre-Calculus
If sinx=-1/2 and x terminates in the third quadrant, find the exact value of tan2x.

Pre-Calculus 12
how to graph y= (x^2-3x-10)/(x-2)

Calculus II
Evaluate the integral by first performing long division on the integrated and then writing the proper fraction as a sum of partial fractions. x^4/x^2-9

Calculus II
Express the integrated as a sum of partial fractions and evaluate the integral 3x2+x+9/(x2+5)(x-6)

Calculus
The prompt for all of these question is "consider the function f(x) = sin^2(x)". Part A: Write the first four terms of the Maclaurin series for f(x). I assumed this implied non-zero terms, so I found x^2-(1/3)x^4+(2/45)x^6-1/315(x^8). I am fairly confident about this. Part B: ...

Math calculus
(2) (-1) (3)+(4)

Math A Calculus
For a =( 2 ÷3)and b=(-1÷4)..Find a).. a+b b).. | a+b | c).. Find the length of the vector i + 2j-- 2k

Calculus
I have to get the result of the serie from 1 to infinite of |sin(4n/π) +3|/ 4^n I really don't know what to do... Please I would really appreciate if anyone can help me

Calculus
Two forces act on an object at 20 degree to each other. One force has a magnitude of 200N, and the resultant has a magnitude of 340N. Determine the magnitude of the second force and the direction it makes with the resultant.

Calculus
A ship is sailing due north at 12km/h while another ship is observed 15km ahead, traveling due east at 9km/h. What is the closest distance of approach of the two ships?

Calculus
Show how the function y = e^(-x) sin x could represent damped oscillation. a) Determine the local extreme for a sequence of wavelengths. b) Show that the local maxima represent exponential decay.

Calculus
Find the area of the region between the curves y=8−x^2 y=x^2 x=−3 and x=3 I made a slight correction

Calculus
Find the area of the region between the curves y=8−x2 y=x2 x=−3 and x=3

calculus
i)f (x)=x^3 + -x^2

calculus
i)f (x )=e^x sinx

calculus
i)f(x)=(x^3 + -x^2 )(x^2 + 2)

calculus
Find the derivatives of the following function: i)y=-3x^-3 +2x^-2 + x-2

physics/calculus
can someone explain to me why the derivative and second derivative of this position vector r=ax+bty is r'=ax' +by'+ bty' ( why is there a by'...?) and r''=ax'' + cy' +cy' +cty'' ( why is there 2 cy' 's?

calculus
Use series to evaluate the limit. limit as x approach 0 [1-cos(5x)]/[1+5x-e^(5x)]

calculus
Evaluate the indefinite integral as an infinite series. [cos(x)-1]/x dx

Calculus
How do we integrate [(cosx)^2(nx)(sin(nx))]/[a-(cos(nx))] dx?

calculus
Find the radius of convergence, R,and the interval, I, of the series. starting n=1 [(x-4)^n]/(n^n)

calculus
Find the interval, I, of convergence of the series n=0 [((-1)^n)(x-5)^n]/(3n+1)

calculus
ind the radius of convergence, R,and the interval, I, of the series. n=3 [x^(n+1)]/(5n!)

Calculus
The base of a solid is a region located in quadrant 1 that is bounded by the axes, the graph of y = x^2 - 1, and the line x = 2. If cross-sections perpendicular to the x-axis are squares, what would be the volume of this solid?

Calculus
Given that the limit as h approaches 0 of (f(6 + h) - f(6))/h = -2, which of these statements must be true? 1. f'(6) exists 2. f(x) is continuous at x=6 3. f(6) < 0

Calculus
Use the midpoint rule with n=4 to approximate the region bounded by y=-x^3 and y=-x Show that the function f(x)= (integral from 2x to 5x) (1)/(t) dt is constant on the interval (0,+infinity)

One more question Calculus
write n with limit from 0 to infinity with the summation n on top and k=1 on the bottom (5+k(2/n))^10 (2/n) as a definite integral.

Write the integral in one variable to find the volume of the solid obtained by rotating the first‐quadrant region bounded by y = 0.5x2 and y = x about the line x = 5.

find the area bounded by the curves y^2=2x+6 and x=y+1

find d/dx (integral from 2 to x^4) tan(x^2) dx tan(x^4)^2*4x^3 MY ANSWER

Calculus
Use the Comparison Theorem to determine whether the following integral is convergent or divergent. S= integral sign b=infinity and a=1 S(9(cosx^2))/ (1+x^2) dx

Calculus
k(x) = f(x^4). Which of the following is k''(x)? a. 2xf''(x^2) b. 4x^2f''(x^2) c. (4x^2+2x)(f''(x^2)) d. 4x^2f''(x^2)+2f'(x^2) e. 4x^2f''(x^2)+2xf'(x^2)

Math (Calculus II) (Volume Revolution Setup)
Take the area enclosed by the curves y = sqrt(x), y = 1, and x = 4. Rotate it around the line x = 5. Find the volume. While I understand the general problem would call for the shell method ∫[a,b] 2*pi*r*h dx With r = 5 - x and h = sqrt(x) - 1 But, what happens say if the ...

Calculus
Find the area of a function using integrals that equals .5 (can range from .499 to .504) There has to be three regions for the equations

One more question Calculus
A car travels along a straight road for 30 seconds starting at time t = 0. Its acceleration in ft/sec2 is given by the linear graph below for the time interval [0, 30]. At t = 0, the velocity of the car is 0 and its position is 10. What is the total distance the car travels in...

Water is poured into a bucket according to the rate F(t)=(t+7)/(2+t), 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 really quick check
The graph of f ′(x) is continuous and decreasing with an x-intercept at x = 2. Which of the following statements must be true? Edit The graph of f has an inflection point at x = 2. The graph of f has a relative maximum at x = 2. The graph of f is always concave down. MY ...

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 so, I took the integral of the equation so from 0 ...

Use the graph of f(t) = 2t +2 on the interval [−1, 4] to write the function F(x), where f(x)= integral from 1 to x f(t) dt f(x)=x^2+3x f(x)=x^2+2x-12 My Answer f(x)x^2+2x-3 f(x)=x^2+4x-8 Find the range of the function f(x)=integral from 0 to x (sqrt 4-t^2) dt (0, 4pi) (0, ...

f is a function that is differentiable for all reals. The value of f ′(x) is given for several values of x in the table below. The table: x -8,-3,0,3,8 f'(x)-4,-2,0,4,5 If f ′(x) is always increasing, which statement about f(x) must be true? f(x) passes through the origin ...

Which of the following functions grows the fastest as x grows without bound? f(x)=x^2 g(x)=x^2+5x <<<<MY ANSWER h(x)=(sqrt x^4+2x) They all grow at the same rate Compare the growth rate of the functions f(x)=4^x and g(x)=(sqrt 16^x+2^x) f(x) grows faster than g(x) ...

Pre-Calculus 12
Write the following expression as a single logarithm: 4 log 3 + 2

Calculus
Set up, but do not evaluate, the integral which gives the volume when the region bounded by the curves y = Ln(x), y = 2, and x = 1 is revolved around the line y = −2.

Math (Calculus II) (Partial Fraction Decomposition
I'm having trouble trying to solve for the partial fraction decomposition in order to find the integral. ∫ x / (x^4 - a^4) dx I'm assuming a is some constant in this case. So I factored the denominator to this: (x^4 - a^4) = (x^2 + a^2)(x + a)(x - a) Which turns each of them...

Write the integral in one variable to find the volume of the solid obtained by rotating the first‐quadrant region bounded by y = 0.5x2 and y = x about the line x = 5. Use the mid-point rule with n = 4 to approximate the area of the region bounded by y = -x^3 and y = -x. A ...

calculus
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) (1/3,1,1/4,1/2,1/5,1/3,1/6,1/4...)

calculus
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) {0, 4, 0, 0, 4, 0, 0, 0, 4, ...}

calculus
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) An=(n^2)(e^-n)

calculus
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) An = cos(n/8)

calculus
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) An=[(-1)^n]/[8[(n)^(1/2)]]

calculus
priya decides to go to the store which is 8km from her house. she first ran at a rate of 7km/h then walked the rest of the trip at a speed of 3km/h. if the total trip took 2hrs how many kilometers did she walk?

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 ...

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.

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

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.

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 ...

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