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Calculus Questions
Find the absolute and local extrema for f(x) = (x^2 - 1)^3 on [-1,2].
Determine an equation of the plane tangent to the surface x2 - 3x + y2 -...
Given the force field F(x, y) = (x − y, 4x + y^2 ), find the...
1a. Find the domain and range of the function. (Enter your answer using interval notation.) f(x)...
Use the method of Lagrange Multipliers to find the extreme value(s) of f(x, y) = 3x...
Using Euler's method Calculate the exact solution and investigate the accuracy of your approximations. dy/dx=x-xy y(1)=0...
Find the average height of the paraboloid z=10x^2 + 7y^2 above the annular region 4<= x^2...
A plane flying horizontally at an altitude of 1 mi and a speed of 480 mi/h...
To determine the surface area of the top part of the sphere x^2+y^2+z^2=4 that is inside...
a particle is moving with the given data. find the position of the particle. a(t)= 10...
The position of a car along a straight track after t seconds is given by s...
If a bacteria population starts with 125 bacteria and doubles in size every half hour, then...
Find the degree 3 Taylor polynomial T3(x) of function f(x)=(7x−5)^3/2 at a=2. T3(x)=
Estimate the instantaneous rate of change of the function f(x)=−x2+2x+1 at x=2 using the average rate...
Find x and y cos x + i sin x = cosh(y -1) + ixy Hint:...
Sketch the graph of the function f(x) = x3 + 3x2 +3x + 5
Use calculus to find the area A of the triangle with the given vertices. (0, 0), (4,...
Evaluate the surface integral S F · dS for the given vector field F and the...
2) A ladder needs to reach a building by passing over a fence that is 8 ft...
Compute the area between y=x^2+1 and y=2-|x|
1) A cable company currently charges $105/month and has 4800 customers. They decide that for every $2...
Find the linear approximation to g(x)=ln(x^2+2x+3) at the critical point x=-1. Then using the same function,...
suppose that f(0) is 0 and derivative of f at 0 is 4. how would you...
Use the method of Lagrange multipliers to find the maximum value of f(x,y) = xy subject...
Find the area of the region that is outside the cardioid r = 1 +cos (theta)...
find the area of the region bounded by the graph of y=x^3-2x^2-x+2 and y=3x^2-5x+2
Let F ( x , y , z ) =< e^z sin( y ) + 3x...
Solve the initial value problem y′=3y2sinx,y(0)=4. y=?
Suppose you borrowed $200,000 for a home mortgage on January 1, 2015 with an annual interest...
Suppose you invested $5,000 in a CD on January 1, 2015 maturing in 20 years that...
Jack and Jill stand in the same spot, but face different directions: Jack faces east. Jill...
Set up integrals to compute the total volume in m^3 of and the total work in...
Find the maximum value and the absolute minimum value of the function f(x)=x^2-(1/x) on the interval...
In the exercise, X is a binomial variable with n = 7 and p = 0.3....
In Exercises 31-42, solve the initial value problem. 3(x^(2))y''-4xy'+2y=0, y(1)=2, y'(1)=1
The path of a total solar eclipse is modeled by f(t) = 0.00302t^2 - 0.516t +...
a.) Can the mean value theorem be used on f(x)= 3x^2 - 6x +2 on [-5,...
In Exercises 21-30, solve the nonhomogeneous Cauchy-Euler equation. (Assume x > 0). (x^(2))y''+2xy'-6y=2x
Find the general solution of the given differential equation. y'' − y' − 2y = −8t...
In Exercises 1-20, find a general solution of the Cauchy-Euler equation. (Assume x > 0). 4(x^(2))y''+17y=0
Find the exact location of all the relative and absolute extrema of the function. HINT [See...
when ı solve the sequences problem in which order should ı apply tests ?
Consider the region bounded by the line y = 2x and the parabola y = 2x2-2x....
Let ? (?, ?) = ? sin (?2 + ?2). Find the following partial derivatives: a)...
Find the volumes of the solids generated by revolving the triangle with vertices left parenthesis 2...
Show work, draw a picture, label your variables. (4pts) We want to construct a box whose...
The Cartesian coordinates of a point are given. (a) (−3, 3) (i) Find polar coordinates (r,...
According to Hooke’s Law, the force required to maintain a spring stretched x units beyond its...
if a baseball is thrown vertically upward with an initial velocity of 128 ft/sec, the ball’s...
Find the local maxima and minima values for the function f(x)= e^(x^5-x^4-2x^3+x^2-1)
A Bernoulli differential equation is one of the form dy/dx+P(x)y=Q(x)y^n (∗) Observe that, if n=0 or...
Determine the equations of two lines that pass through the point (-1,-3) and are tangent to...
Given ?=?^(−?) and ?=??^(6?) find the following derivatives as functions of ?. dy/dx= d2y/dx2=
Topic: Differential Equations, Laplace Transform, particular solutions Please explain what is a Laplace transform, why it...
Consider the following vector function. r(t) = 6t2, sin(t) − t cos(t), cos(t) + t sin(t)...
3) Portfolio optimization in practice: What are the two options for an investor who as a...
In Exercises 1-20, find a general solution of the Cauchy-Euler equation. (Assume x > 0). 2(x^(2))y''-8xy'+8y=0
Maximize Q=xy, where x and y are positive numbers such that x + 4/3y^2 = 9....
If the solution of a difference equation is yn=-15.625+18.425(3.4)n , then determine the difference equation (with...
25) Let h(t)=tan(4t+7). Then h'(3) is and h''(3) is
Consider the surface S parametrized by the equations x = uv, y = u + v,...
In this problem, p is the price per unit in dollars and q is the number...
The position s of a point (in feet) is given as a function of time t...
1) show that tanh-1(x) = 1/2 ln (1+x/1-x) 2) show that a) d/dx (cosh-1(x)) = 1/sqrt...
Let be the problem with initial value f(t,y) = yt3 , y(0)=1 Write the general formula...
Is it possible for a continuous function to attain an absolute maximum on a closed interval...
From a thin piece of cardboard 40in by 40in., square corners are cut out so that...
Find the area of one petal of r = 5 cos3 θ.
Please use the second derivative test to determine whether each point is local min/max or saddle...
related rates An upside down cone is being emptied at the rate of 4 cubic feet...
An energy drink container in the shape of a right circular cylinder must have a volume...
the curve shown below has parametric equations : x = t2 - 2t +2, y =...
A tank in the shape of a circular paraboloid with top radius 3m and height 9...
Suppose that you are throwing a surprise birthday party for your favorite person or animal. One...
Suppose the radius, height and volume of a right circular cylinder are denoted as r, h,...
Use the given transformation to evaluate the integral. 8x2dA, R where R is the region bounded...
Find the intervals on which the graph of f is concave upward, the intervals on which...
solve the following system and classify it consistent or inconsistent ×+3y+3z=8 x-y+3z=4 2x+6y+6z=16
Find the Volume of the solid obtained by revolving the region bounded by y=-x^2+1, the x-axis,...
1. Find the area of the shaded region. 2. Find the limit. Use l'Hospital's Rule where...
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