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Calculus Questions
Find the work done by the force field F(x,y,z)=6xi+6yj+7k on a particle that moves along the...
Use the Table of Integrals in the back of your textbook to evaluate the integral. ∫...
A bag contains 6 red balls and 9 white balls. Two balls are drawn without replacement....
Two balls are drawn from a bag containing 4 white balls and 3 red balls. If...
Verify that the function f(x) = 5x 3 − 2x − 4 satisfies the hypotheses of...
Consider that for ‘x’ units sold, the total REVENUE function is : R(x) = 75x2– 15x...
Questions 1 - 4: Consider the function ?(?) = −?^3 + 1 over the interval [-1,3]....
Given ?(?) = 3√?.(cube root of x) Give a bound on the magnitude of the error...
One car leaves an intersection traveling north at 48 mi/h. Later, a second car leaves that...
A commercial cherry grower estimates from past records that if 25 trees are planted per acre,...
Bismuth-210 has a half-life of 5 days. A sample originally has a mass of 160mg a)...
Show that an undirected graph G = (N,A) is connected if and only if for every...
A painting is hung on a wall in such a way that its upper and lower...
The rate of depreciation dV/dt of a machine is inversely proportional to the square of t+1,...
the function f(x) = ex - 2e-2x - 3/2 is graphed at right. evidently, f(x) has...
What is the relationship between the directional derivative, the gradient, partial derivatives and the vector component?
Find the (a) slope and (b) equation of the tangent to the curve at the point...
Solve the equation y''' + 4y = sec(2t), -pi/4 < t < pi/4
In an electronic device, individual circuits may serve many purposes. In some cases, the flow of...
Let a>0 & b>0 be two positive numbers and consider the function f(x) = x^a+x^−b. Find...
1. Use the first derivative test and the second derivative test to determine where each function...
Evaluate (if possible) the vector-valued function at each given value of t. (If you need to...
find the absolute maximum value and absolute minimum values of the function f(x,y)4xy^2-x^2y^2-xy^3 on the set...
let P be the point on the line y=4.65x+4.18 which is closest to the orgin. find...
(1) The volume of a cube is increasing at a rate of 10 cm3/min. How fast...
For 1 and 2, give a function f that satisfies the given conditions. 1. f '...
Let F(x, y, z) = (yz, xz, xy) and the path c(t) = (cos3 t,sin3 t,...
Let f(x)=8x2−32x+13 (a) Find the critical point c of f and compute f(c) (Use symbolic notation...
find the eigenvalues and eigenfunctions for the given boundary-value problem. y'' + (lambda)y = 0, y(-pi)=0,...
Solve the initial value problem. (?2+1)?′+2?=1+?where?(0)=2(x2+1)y′+2y=1+xwherey(0)=2
(1)Suppose that the DERIVATIVE of R(X) ( i.e., R PRIME OF X) ) equals: R’(X) =[...
given the conditions for a function (f(x)) f '(x) > 0 on (0,3) • f '(x)...
Consider the function f(x,y) = (e^{2x})lny whose domain is {(x,y): y>0}. What is the equation of the...
The number of cases of students infected with MRSA on a university campus x days after...
The average ticket price for a concert at the opera house was $20. The average attendance...
Use the method of laplace transforms to solve the following Initial Value Problem: y"+2y'+y=g(t), y'(0)=0
Let H be the hemisphere x2 + y2 + z2 = 17, z ≥ 0, and...
Find the derivative of y=x^3x using the methods of example 6 dy/dx=
Please show me a problem with solution in solving the centroid of a miscellaneous solid
About convex function: Please show that f(x) = 1/2·xTQx+aTx is a convex function if and only...
Suppose that one factory inputs its goods from two different plants, A and B, with different...
For the questions below, consider the following function. f (x) = 3x^4 - 8x^3 + 6x^2...
I need to evaluate the double integral:I from 0 to 3, I from 0 to sqrt(9-y^2),...
find the Interval of convergence of 1. sum from {0}to{infinity} X ^ 2n / 3^n
f'(–2 ) and (ii) f"(–2 ) , where f(x) = √ 5 – x2 – x3
Solve for x. (Enter your answers as a comma-separated list.) ln(x) + ln(x + 4) =...
Consider the hemispherical shell of inner radius 3 and outer radius 7. The mass density at...
tan^-1(5x^2y)=x+2xy^2
Which of the following is the right hand sum with n=3 rectangles for ?(?)=?? on the...
1. Consider the function f(x) = x 3 + 7x + 2. (a) (10 pts) Show...
The average value of a positive function over an interval [a,b] is given by the area...
1. Find the distance between the point and the line given by the set of parametric...
Find the gradient of the function and the max value of the directional derivative at the...
Use the Chain Rule to find dw/dt. w = ln x2 + y2 + z2 , x...
Derive explicitly the three-step and four-step adams-moulton methods and the three-step adams-Bashforth method. The two methods...
Let f(x) = 3x^5/5 −2x^4+1 Find the following -Interval of increasing -Interval of decreasing -Local maximum(s)...
Can you show steps as well? At least for one so i can practice and check...
Can someone think of 2 simple examples of a function that has a vertical asymptote in...
Let f(x) = x 1/2 (3−x). Find the absolute maximum and absolute minimum values of the...
Please answer the following questions. You may use the back of the page if necessary. You...
Integrate G(x,y,z) = xy2z over the cylindrical surface y2 + z2= 9, 0 ≤ x ≤...
Please answer the following questions. You may use the back of the page if necessary. You...
Find the absolute maximum and minimum values of f(x,y)=2x^2+y^2-xy^2 on the triangular region shown with vertices...
4) Use implicit differentiation to find the equation of the tangent line to the curve xy^3+xy=16...
A tank cannon fires from an initial height of 8 feet with an initial velocity of...
Find all critical numbers, the open intervals on which f(x) is increasing or decreasing, and locate...
1. Find the constants a and b so that the function f is continuous, where f(x)...
We are given a level surface F ( x , y , z ) = 0...
1) Find the interval of convergence I of the series. (Enter your answer using interval notation.)...
Find the general solution of the system dx/dt = 2x + 3y dy/dt = 5y Determine...
Find the value of the directional derivative of the function w = f ( x ,...
if f''(x)= -cos(x)+sin(x), and f(0)=1 and f(pi)=), what is the original function
S is a region on the plane 7x + 8y + 3z = 4 contained within...
a) What is the average value of f(x) = √ 1 − x^2 over the interval...
For full credit be sure to show all work and units. 1. A 20 foot ladder...
The force exerted by an electric charge at the origin on a charged particle at a...
Find all functions f(x) such that ? ′(?) = ?? − ?^ −? , ?(?) =...
Investigate the convergence or divergence of the series. Justify your answer. E (3)/(2n-n)
let f(x,y) = xe^(xy) Find the directional derivative of f at point (2,0) in the direction...
The number of subscribers in a small community to a cable TV provider company is linearly...
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