Calculus Questions

##### The revenue and cost function are given. R(x) = 35x − 0.35x2; C(x) = 4x +...

##### Find the derivative of the function using the definition of derivative. f(x) = 1 5 x...

##### Scenario: You are the manager of a company that manufactures electric chainsaws. Currently the company makes...

##### Scenario: You are the manager of a company that manufactures electric chainsaws. Currently the company makes...

##### Change from rectangular to cylindrical coordinates. (Let r ≥ 0 and 0 ≤ θ ≤ 2π.)...

##### A bucket begins holding 25 kgs of sand. The bucket is to be lifted to the...

##### 4 pts) Find the value of dy dx at the point (1,4), where y^2 = 2...

##### The production function for a company is given by f(x, y) = 100x0.6y0.4 where x is...

##### Find the following limit. Is the function continuous at the point being approached? ModifyingBelow lim With...

##### (uxv) is orthogonal to (u+v) and (u-v) u and v are nonzero vectors not sure where...

##### find the value of x for which the series converges sigma (x+7)^n for n=1 to n=infinity

##### use the Chain Rule to find ∂w/∂s for w=e^xcos(y) where x=s^2sin(t) and y=s/t

##### Estimate f(2.1, 3.8) given that f(2, 4) = 6, fx(2, 4) = 0.2, and fy(2, 4)...

##### In the 2000 U.S. Census, a small city had a population of 45,000. By 2010, the...

##### A manufacture has been selling 1000 television sets a week at $510 each. A market survey...

##### Solve step by step please Let ?: ? → ? be a function. Show that ?...

##### Find the indicated partial derivative(s). f(x, y) = x8y9 − x7y8; fxxx, fxyx

##### Suppose that a mass suspended on a string has the following equation of motion x(t) = ...

##### Find parametric equations for the rectangular equation y = e^x + 9 using the parameter t...

##### (a) Find the value of ω for which we can observe resonance in the solution of...

##### 7. Two cars start moving from the same point. One travels north at speed of 15...

##### A ladder 25 feet long is leaning against the wall of a house. The base of...

##### Find the area of a triangle with vertices A (1, 4, -1), B (-1, 2, 0),...

##### Describe the x-values at which the function is differentiable. (Enter your answer using interval notation.) y...

##### (1 point) Gandalf the Grey started in the Forest of Mirkwood at a point with coordinates...

##### If f ″(x) = (x − 1)^5 (x − 2)^7 (x − 3)^6, how many inflection...

##### A company operates two plants which manufacture the same item and whose total cost functions are...

##### Find the minimum and maximum values of the function f(x,y)=x2+y2 subject to the constraint x4+y4=2592 Use...

##### Find the constant a such that the function is continuous on the entire real line. f(x)...

##### A horizontal mass spring oscillator is constructed, where the mass of the oscillator is 3 kg,...

##### Using the method of undetermined coefficients, solve the following IVP y″ + y′ = f (x) ...

##### Solve below differential equation d2ydx2+2dydx+3y=2sin2x coefficients of final answer/s should be exact. Ie radical/fraction form Find...

##### A searchlight 60 ft from a straight wall is rotating at a constant angular rate. If...

##### Find the equilibrium solution to y'= (y^2-2y+1) (x^2-4)

##### vert symptotes f(x)=tan(3x)

##### An epidemiologist is investigating two suspected risk factors for a deadly disease (“wasting disease”). One of...

##### Problem #16: Use the Laplace transform to solve the following initial value problem, y′′ − 5y′...

##### 3. Find the volume of the solid of revolution. The region is bounded by y= 4x...

##### Use the Maclaurin series for e^{-x^{2}} to approximate e^-4 to 2 decimal places

##### Find the flux of the vector field F = x i + e6x j + z ...

##### Question 6. Find the distance from point P(1,−2,3) to the plane of equation (x−3) + 2(y...

##### x/(x^2+5) Find concave upward and downward

##### The displacement (in centimeters) of a particle moving back and forth along a straight line is...

##### Find the area inside one loop of r=2cos(5θ)

##### Use the price-demand equation below to determine whether demand is elastic, is inelastic, or has unit...

##### Suppose ?(?,?)=??f(x,y)=xy, ?=(−4,−4)P=(−4,−4) and ?=3?+2?v=3i+2j. A. Find the gradient of f. ∇?=∇f= ?+i+ ?j Note: Your answers should...

##### A tank in the shape of an inverted cone 12 feet tall and 2 feet in...

##### For the curve x = t - sin t, y = 1 - cos t find...

##### The derivative of the function has three roots: -1, 2, and 4. That is, and there are...

##### For the function g(x)=5x2+x A. Find the instantaneous rate of change at x=-3 B. Find the...

##### find the general solution to the ODE: y''+yx^2 =0

##### What is the equation of the line which passes through the point ( x 0 ,...

##### For which of the following expressions is y a function of x? Select all that apply....

##### Use an infinite series about ?=0 to find two solutions of the differential equation: ?′′+2??′−?=0

##### F(x)=4x-x^2 x= 0 to 2 two sub intervals Approximate the area under the curve over the...

##### Find the area of the region that is enclosed between ?=3sin(?) and ?=2cos(?) from ?=0 to...

##### Find the volume of a solid of revolution that is formed by rotating about the y-axis...

##### find the volume of the solid obtained by rotating x=1+(y-2)^2 and x=2 about x-axis

##### Known f (x) = sin (2x) a. Find the Taylor series expansion around x = pi...

##### Use the Laplace transform to solve the following initial value problem, y′′ − 5y′ − 36y ...

##### A tank contains 90 kg of salt and 2000 L of water: Pure water enters a...

##### Eliminate the parameter to find a Cartesian equation of the curve. Then sketch the curve and...

##### For parts ( a ) − ( c ) , let u = 〈 2 ,...

##### Solve the initial value problem 8(t+1)dy/dt - 6y = 12t for t > -1 with y(0)...

##### x’’+x=4cos8t, x(0) =1, x'(0) = 0 use Laplace transformations to solve the following initial value prob

##### Write the equation ( in terms of x and y) of the tangent line to the...

##### Find the volume of the solid by subtracting two volumes, the solid enclosed by the parabolic...

##### Consider the functions f (t) = e t and g(t) = e−3t defined on 0 ≤ ...

##### 1. In this problem, you consider a small computer company. (a) The company estimates that the...

##### 10.) (23 pts.) Verify the Divergence Theorem for P(x, y, z) = (y) i+ (—x) j...

##### Let f(x, y) = 2x^3y^2 + 3xy^3 4x^3 y. Find (a) fx (c) fxx (b) fy...

##### An open-top box has a square bottom and is made to have a volume of 50in^3....

##### Find the volume of the solid generated by revolving the following region about the given axis....

##### Find the vectors T and N and the binormal vector B = T ⨯ N, for...

##### Find an equation for the line L that contains the point the point P = (−1,...

##### Determine the value of the area formed by the figure limited by the functions y =...

##### 1.) For y = f ( x ), the __________ from x = a to x...

##### Find parametric equations for the tangent line to the curve with the given parametric equations at...

##### Consider the vector a(t)=〈cost,sint〉 with components that depend on a real number t. As the number...

##### 5. (a) Find the length of the given line, C, using calculus and the arc length...

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