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Calculus Questions
What is integration in calculus and why is it important?
a. Determine an equation of the line of intersection of the planes 4x − 3y −...
consider the region r bounded by the parabola y=4x^2 and the lines x=0 and y=16 find...
Find the volume of the solid generated by revolving the area bounded by the given curves/lines...
1) Find the arc length of the graph of the function over the indicated interval. Show...
Design a cylindrical can (with a lid) to contain 5 liters (= 5000 cm3) of water,...
Solve the di↵erential equation (t)dy/dt + 2y = 4t^2-3t + 4 subject to the initial condition...
Let V be the volume of a cylinder having height h and radius r, and assume...
Let f(x) = 5x + tanh(x), where tanh x = sinh x /cosh x , and...
Consider f(x, y) = (x ^2)y + 3xy − x(y^2) and point P (1, 0). Find...
Does the line with equation (x, y, z) = (5, -4, 6) + u(1,4,-2) lie in...
use the squeeze theorum to show that *** please show work limx→0 cos(x)x^8 sin(1/x)=0 limx→0 tan(x)x^4...
Determine the normal form of the plane containing the point ((3.91 + 0.03), (0.5 + 0.5),...
Please write down the details of reasons for your solutions. Thanks. Questions 2 a) Let f(x,y)...
use the intermediate value theorum to show that the following functiom has a root. f(x)= tan(x)+x-1...
Use the disks and washers (or shell) method to calculate the volume of the solid by...
find the absolute maximum and minimum values of the function f(x) = 10x / 1+64x^2 on...
Find the equation of the line tangent to the graph of x^(4)y-xy^3 = -324 at the...
Find an equation of the tangent plane to the given parametric surface at the specified point....
Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per...
The region bounded by the given curves is rotated about the specified axis. Find the volume...
1). Consider the following function and point. f(x) = x3 + x + 3; (−2, −7) (a)...
A baseball team plays in he stadium that holds 66000 spectators. With the ticket price at...
solve: x2y' + x2y = x3 y(0) = 3
Solve the initial value problem y' = 3x^2 − 2y, y(0) = 4
SupposeG=〈y2,−x2〉. Find both the circulation and flux of the field G around and across C. Briefly...
Determine which of the differentials (or both) is the total differential: a) (yex +ey –2)dx+(ex +xey...
A University’s math department offers two courses: Finite Math and Applied Calculus. Each section of Finite...
A balloon leaving the ground 80 ft from an observer, rises 10 ft/sec. How fast is...
Find the equation of the plane that contains the line (x-2)(1/3)=(y)(1/2)=(z+4) and passes through the point...
Question : y'' = 4y' + 13y =0 , (y''+ 2y' + 2y)^2 = 0 ,...
A tank shaped like a cone pointing downward has height 9 feet and base radius 3...
Find the solution y'' + 4w2y = 0, y(0) = -1, y'(0) = 2w
the integration factor of : (1+5xy^2)dx+(x^2)ydy=0
Evaluate the following integral using trigonometric substitution. a) Rewrite the given integral using this substitution. b)Evaluate...
Q3: A) Verify that the hypotheses of the Mean Value Theorem are satisfied on [0,2] and...
Q1: Sketch the graph of polynomial ?(?)=?3−?. Label the coordinates of the x- and y-intercepts, stationary...
If 27 J of work are needed to stretch a spring from 10 cm to 16...
A rocket is fired at an angle of 25° to the ground and with an initial...
5. The height s at time t of a silver dollar dropped from the top of...
Assume that the price and the demand are both positive. Use the price-demand equation, x= f(p)= √(1600-2p^2)...
Find the area of the surface generated when the given curve is revolved about the y-axis....
A glass window has the shape of a trapezoid with height 4m, width at the top...
When a murder is committed, the body, originally at 37 degree Celsius, cools according to Newton’s...
The Deligne Dam on the Cayley River is built so that the wall facing the water...
A tank in the shape of a sphere with radius 4 ft. is half full of...
Tell me a function who's antideridative is not possible
Find an equation of the plane. The plane that passes through (7, 0, −4) and contains...
please make writing legible Evaluate ∫?2 sin? dx
Draw a graph of the triangle having vertices at (−1, 0) and (1, 1) and (2,...
Find the inverse Laplace transform of F(s)=5s2-3s+25/(s-2)(s2+9)
Let f(x)=5+3/x a) Find f′(x) b)Find the slope of the tangent line at x=1. Slope =...
Solve the initial value problem y = 3x^2 − 2y, y(0) = 4
Find the Taylor degree 4 polynomial of ? (?) = −? ∗ ??? (?) centered on...
What are Singular solutions in differential equations.. How to find them.Can we find them using the...
Let R denote the region that lies below the graph of y = f(x) over the...
Use Lagrange Multipliers to find the extreme values of f(x, y, z) = x + 2y^2...
Find the absolute maximum and minimum values of f(x, y) = 4xy + x^2 on the...
Let R be the finite region bounded by y=x^3 and y= 9x. (a) Write an integral...
At the time of the birth of a child, a parent wants to begin a college...
A chemist has two large containers of sulfuric acid solution, with different concentrations of acid in...
Let f(x) = 5x2 + x − 2. Use the limit definition of f′(a) and the...
Region 2: Draw the region bounded by y=sqrt(x-2) and x-4y=2 . Draw a representative rectangle and...
Find the equation of the osculating circle at the local minimum of f(x)=3x^3−5x^2+(0/1)x+5
5) A rock is thrown directly southeast (45 degrees to S and E), at an initial...
The value of the integral ∫C(3x2+ycosx)dx+(sinx−4y3)dy∫C(3x2+ycosx)dx+(sinx−4y3)dy, where CC is an arbitrary path from A(−π,−1)A(−π,−1) to B(2π,1)B(2π,1),...
a) find dy/dx for each of the following i. y = 4ex (1 + ln x)...
Find the linear approximation L(x) to y = xsinx for values of x near a =...
What is the step by step integration for (x+1)/(x2+x+1)?
Find the ?? (?) Taylor polynomial of ? (?) = (? - ?) ?? (? -...
Suppose the sale price of a used car can be predicted by a function f(x, y)...
find the explicit particular solution of the initial value problem 2*x^1/2(dy/dx)=(cos^2)*y y(4)=pi/4 differntial equations
You are given a supply function of s(q)=5qs(q)=5q and a demand function of d(q)=−q2+36d(q)=-q2+36. Find the...
Let f1, f2, f3: [a,b] -->R be nonnegative concave functions such that f1(a) = f2(a) =...
An employment research company estimates that the value of a recent MBA graduate to an accounting...
Graph the polar equations on a single polar graph. Show all your work. You may use...
Evaluate the line integral, where C is the given curve. z2dx + x2dy + y2dz, C...
Use Green's Theorem to evaluate the line integral along the given positively oriented curve. C 9y3dx...
#5) (Please be as clear as possible in your answer and write as big and neatly...
y"+8(xy'+y)=0 Verify that yı = exp(-8x²/2) is one solution find the general solution in the form...
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