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Calculus Questions
Find the volume of the solid generated by revolving the region bounded by the given curve...
For the function f(x)=x^3+5x^2-8x , determine the intervals where the function is increasing and decreasing and...
For the equation given below, evaluate y′ at the point (1,2). (3x−y)^4+4y^3=33. y′ at (1,2) =
Find the indicated maximum or minimum value of f subject to the given constraint. Minimum: f(x,y)=2...
Find the solution of the initial value problem y′′+5y′+6y=0, y(0)=11 and y′(0)=-25
A Ferris wheel is 15 meters in diameter and boarded from a platform that is 5...
if x^2+y^2=1, find an expression for d^2y/dx^2
if x^4+y^4=1, find the expression for d^2y/dx^2
(a) Find parametric equations for the line through (5, 3, 6) that is perpendicular to the...
Two cars are approaching an intersection on roads that are perpendicular to each other. Car A...
how do I show if the series sigma(n=1 to infinity) cos(npi/3)/(n!) is divergent, conditionally convergent, or...
integral 1/secx-1dx
Given S is the surface of the paraboloid z= 4-x^2-y^2 and C is the curve of...
find the volume of the solid obtained by rotating the region bounded by the graphs of...
The marginal cost in dollars is given by dc/dx=4x +3. If the fixed costs are $2000...
Solve: (x^4 – xy^3)dy + (2y^4 – x^3y)dx = 0
A parametric curve r (t) has the property that r ″ ( t ) = (...
Let R be the tetrahedron bounded by the planes x=0, y=0, z=0 and 33x+7y+2z=8. The volume...
Use implicit differentiation to calculate the slope of the tangent to the curve given by sinh(xe ...
If f(x) = 3x2 − x + 5, find the following f(2) = f(−2) = f(a)...
Discuss the purpose, function, and problems with using the MyPlate Planner.
Find, correct to the nearest degree, the three angles of the triangle with the given vertices....
Find Cartesian equation of a plain through the point a and parallel to the given vectors...
3. Given f(x) = arctan x and g(x) = e^x , find the following: a. (f...
Find the ABSOLUTE MAXIMUM value of the function on the closed interval .
Let P(t) represent the number of people who have been infected by a disease t day...
Use linear approximation to estimate (0.97)3 - 3(0.97)2 without using a calculator.
A one-product company finds that its profit, P, in millions of dollars, is given by the...
Solve the following initial value problem. y′′ − 9y′ + 20y = 3x + e5x, y(0) = ...
Let w = (x 2 -z)/ y4 , x = t3+7, y = cos(2t), z =...
The curve y = x4 - 4x3, where is it increasing, where is the inflection point...
6) You may answer the following questions using the appropriate C(n,r)’s and or P(n,r)’s. It is...
Using what you know from Calculus 3 Find the equation of the plane parallel to the...
1)Find the Taylor series for ?(?) = sin ? centered at ? = ? and then...
(1 point) The tank in the form of a right-circular cone of radius 7 feet and...
Consider the function ?(?) = ?^2 − 3? − 2. a) Use Newton’s Method to estimate...
Under ideal conditions a certain bacteria population is known to double every five hours. Suppose that...
Set up an iterated integral for the surface area of the part of the plane x...
Solve the following initial value problem. y′′′ − 21y′′ + 135y′ − 243y = 0, y(0) = ...
Make a substitution to express the integrand as a rational function and then evaluate the integral....
Find general solution to the equations: 1)y'=x-1-y²+xy² 2)xy²dy=(x³+y³)dx
Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of...
\Given f(x)=2sinx+x on [0,2π] (a) Find f′′(x) (b) Find the intervals where f is concave up...
Find, correct to the nearest degree, the three angles of the triangle with the given vertices....
1, Find the area enclosed by the lemniscate of bernoulli r^2 = 9cos (2theta) 2. find...
Find the area of the parallelogram with vertices A(−1,1,3), B(0,3,5), C(1,0,2), and D(2,2,4). Area:
Evaluate : lim ?+3 ;?≥3 ; ?<3 ?→−3 √3?2−2 − 5
If f is continuous on ( a , b ) and f ( x ) ≠...
Find a general solution to the differential equation. y''-6y'+9y=t^-7e^3t. The general solution is y(t)=
Use the Chain Rule to find the indicated partial derivatives. u = r2 + s2 , r...
Find the area between the two curves ?(?) = ? − 5 and ?(?) = 3?...
You are testing a prototype loudspeaker for your Audio division, which may possibly be used in...
Find the charge on the capacitor in an LRC-series circuit at t = 0.02 s when...
The next problem had two decision variables (X and Z). Find the value for x and...
Find the volume (in cu units) of the solid bounded above by the surface z =...
Figure out if the series Σ∞ n=1 (((n + 1)^426) / n! ) converges or diverges....
calculate ∫ e^-rt sin (wt) dt
You are studying the age of an vase that you are using an element, having a...
An airplane takes off at sea level where the air temperature is 15○ C. As it...
1. Determine whether the series is convergent or divergent. a) If it is convergent, find its...
A company has a variable cost of $28 to make x units of an item and...
3) A television is advertised for $2000 cash or on terms of 10% deposit and $80...
f(x)= 3x ^ 2 -4 Find the equation of the tangent line to this function at...
If f(x)=sqrt(x)sin(x) What is the derivative of this function?
I'm studying Erwin Kreyszig's advanced engineering Mathematics and I have an homework, how can I solve...
1. The derivative of y=e−6x+sin3xy=e−6x+sin3x is ________ 2. The derivative of y=e512x+sec18xy=e512x+sec18x is ________ 3. The...
A zoo supplier is building a glass-walled terrarium whose interior volume is to be 2048 ft3....
Use what you learned from the derivatives of f(x)=2^x and g(x)=4^x to make a more general...
use the limit of a sum process to find the net area of the region bounded...
Let f(x,y,z)=exy4z5+xy2+y3z Calculate. fx fy fz fxx fxy fyy fxz fyz fzz fzyy fxxy fxxyz 1
Let u = <3, 2, 5> and v = <-2,5,4> Compute the angle between u and...
Find extrema of f(x,y) = 2x4 −xy2 +2y2, on R = {(x,y) : 0 ≤ x...
Find the angle between the plane x+y+ 2z = 6 and the line x-1 = y-3...
A company anticipates selling 5500 units of a product at a uniform rate over the next...
Find?: ?′′(?) = ?^6 − 4?^4 + ? + 1
f(x)=2x3-10x. Is f(x) increasing or decreasing at x= -1.
A) If h(t) = -16t2 + 64t + 100, t in seconds, describes a stone falling...
a contagious disease is spreading in a town of 2786 people with logistic growth k=0.000017 what...
A population of rabbits oscillates 18 above and below average during the year, hitting the lowest...
Given the parametric equations: x(t) = ?^2 − ? + 2, ?(?) = ?^3 − 3?...
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