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Calculus Questions
Identify the following series as convergent or divergent. State which test you are using, and show...
Find the equation of the tangent plane and normal line to the curve 2z−5=ln( x 2...
Acrosonic's production department estimates that the total cost (in dollars) incurred in manufacturing x ElectroStat speaker...
Use the method of cylindrical shells to find the volume V generated by rotating the region...
Find the mass and center of mass of the lamina that occupies the region D and...
A trough is 10 ft long and its ends have the shape of isosceles triangles that...
Find the solution to the boundary value problem: d2y/dt2−4dy/dt+3y=0, y(0)=7,y(1)=8 y=
Find the local maximum and minimum values and saddle point(s) of the function. If you have...
Consider the differential equation x^2 y' '+ x^2 y' + (x-2)y = 0 a) Show that...
Find the first order Taylor polynomin of f(x,y)=x^2e^y at (0,0) T1(x,y)= Find the second orser Taylor...
Find a power series representation for the function; find the interval of convergence. (Give your power...
An isosceles triangle has a base of 6 units, and an area of 36 units squared....
Consider the following. f(x)=ln(1-x) a) Determine the fourth Taylor polynomial of f(x) at x = 0....
Determine the third Taylor polynomial of the given function at x = 0. f(x)=1/x+3
Use the definition of a Taylor series to find the first four nonzero terms of the...
Solve the given initial-value problem. y'' + x(y')2 = 0, y(1) = 5, y'(1) = 2...
A baseball player 5ft. above the ground hits a ball. The ball flies in a 30°...
Describe the x-values at which f is differentiable. (Enter your answer using interval notation.) f(x) =...
Explain why a limit does not exist when x approaches to 2 for f(x) = √2...
1- Is the formula for the general power derivative given below correct. if not, what term...
A bookstore expects to sell 400 calculus textbooks during the next year. It costs $4 to...
In class I gave a general formula for derivative of an exponential function f(x) = loga...
If two resistors with resistances R1 and R2 are connected in parallel, as in the figure...
Find the extremum of f(x,y) subject to the given constraint, and state whether it is a...
#2. An isosceles triangle has a base of 6 units, and an area of 36 square...
Let g (x) = [(x^2-3)/(x^3)] (a) Determine (if they exist) the vertical and horizontal asymptotes of...
Evaluate the integral using Partial fraction decomposition (PLEASE SHOW EVERY STEPS: the dummy decomposition form, specific...
An isosceles triangle has a base of 6 units and an area of 36 square units....
Let S be the region between •x=1, •x=3, •y=6−(x−2)2, and •y=x 2+1. a) Set up an...
Consider two non-negative numbers x and y such that x+y=10. What is the maximal value of...
The speeds of vehicles on a highway with speed limit 90 km/h are normally distributed with...
Express the given integral as the limit of a Riemann sum but do not evaluate: the...
Give your answer to two decimal places 1) Find the curvature of the curve r(t)=〈 5+...
For the equation ?^(4/6)+?^(2/4)=7. Find the equation of the tangent line at the point (1,36). (Use...
Find the critical numbers of the function. (Enter your answers as a comma-separated list. Use n...
f(x) =x2 -x use f'(x)=lim h->0 f(x+h) - f(x)/h find: 1. f '(x) 2. f '(2)...
1. When a commercial bakery employs w full time bakers, the daily costs, in dollars, is...
1- Find f. f '''(x) = cos(x), f(0) = 8, f '(0) = 6, f ''(0) = 5 2-...
Solve an engineering technology application of a separable differential equation. Use first order linear differential equations...
1. Given an ellipsoid with equation (x−5)^2 /16 +(y−10)^2/ 9+(z−6)^2/ 16= 1 and the plane with...
Find the local maximum and minimum values and saddle point(s) of the function. If you have...
Find the area inside the polar curve of r = 1 + 2 sin θ but...
Determine whether each of the following series converges or not. (Name the test you use. You...
find the work done in the force camp F(x,y,z)=<xz,xy,zy> in a particle that moves along the...
Assume that the radius rr of a sphere is expanding at a rate of 14 in/...
Suppose the derivative of a function f is f '(x) = (x + 1)2(x − 4)3(x...
z= XsinX + XsinY + YsinX find d2z/dx2 find d2z/dy2 find d2z/dxdy
A rectangle is inscribed with its base on the x-axis and its upper corners on the...
Given the function f(x)=x+3/x-4. Answer the following questions. If there are extra blanks, enter NONE 1....
Use the Integrating Factor Technique to find the solution to the first-order linear differential equation (1...
Describe the shape of the parametrically defined curve (eg, upper half of circle with radius =...
Find the relative extreme values of the function. (If an answer does not exist, enter DNE.)...
Find the work done by the vector field F = 〈 2 xy + z/y ,...
In a certain memory experiment, a person is able to memorize M words after t minutes,...
Find equations of all lines having slope negative 1 that are tangent to the curve y...
Given the polar curve: r = cos(theta) - sin(theta) Find dy/dx
Find any values of c where the function f(x)=2x2+3x−4satisfies the conclusion of the Mean Value Theorem...
Suppose you have a cylindrical water tank with a height of S meters with a height...
a spring has a natural length of 40cm. If a 50 Newton force is required to...
the vertex, domain, and range of y=(x+2)^2 +3
1)Consider the function f(x)f(x) whose second derivative is f″(x)=9x+8sin(x). If f(0)=4 and f′(0)=2, what is f(5)?...
Use the Theorem of Pappus to find the volume of the given solid. The solid obtained...
A small company builds tables and chairs. Let x equal the number of tables made each...
Find the length of the r = 1+ cosθ cardioid between 0 ≤ θ ≤ π.
If f, g are differentiable at a, then prove the sum and product rules for derivatives.
Which value of c satisfies the conclusion of the MVT for the function f(x)=4x^2+6x-7 on the...
Differentiate the function. a) f(x) = x5 − 4x + 5 b) h(x) = (x −...
Find the derivative of f(x) = 3^(x ln x) and f(x) = ln( 1/ x )...
Determine the absolute maximum and minimum values of the function f(x)= e^-x^2 over the interval [-2,1].
2. Show that each given function is a probability density function and find the indicated probabilities:•...
A beehive lies inside a chicken wire cage described by the equation x2 +y2 +z2 =...
Given the triangle with vertex (7, -1, -2), (6, -2, -3), (7, -3, -2) find the...
Solve the initial value problem x^2 y ' ' − 9 x y ' + 25...
Find the interest rate needed for an investment of $6,000 to grow to an amount of...
Use Stokes" Theorem to evaluate (F-dr where F(x, y, z)=(-y , x-z , 0) and the...
a particle moves so that r(t)=3sin(t)i+3cos(t)j-3t^2k. find the speed at time t=2
Find y as a function of t if 121y′′−110y′+29y=0 y(3)=6, y′(3)=1. y=
Suppose that the growth rate of the population of city X is proportional to the population...
A mass weighing 24 pounds attached to the end of the spring and stretches it 4...
Evaluate double integral Z 2 0 Z 1 y/2 cos(x^2 )dx dy (integral from 0 to...
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