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Calculus Questions
Given ?(?,?) = sqrt(x + y) a). What’s the domain and range of f(x, y)? b)....
Given?(?,?)= 9− ?^2 a). State the function’s domain and range. b). Sketch the surface in 3-D....
A loaf of bread is removed from an oven at 350◦F and cooled in a room...
Let f(x) = cosh(x). Show that, on any interval [a, b], the arclength of f(x) in...
Consider ∫c x2ydx + x3dy where C is the line segments going from (0,0) to (1,0)...
find the point on the line x+2y=4 that is closest to the point (-1,2).
let f(x)= /4x-3/ i) find f'(x) ii) find the x-values where f(x) is continuous (interval notation)...
A 10 ft3 capacity rectangular box with open top is to be constructed so that the...
Create a bucket by rotating around the y-axis the curve y=3ln(x-6) from y = 0 to...
Find the open intervals on which the function is increasing or decreasing. (Enter your answers using...
Graph the curve (? = −2 cos ? , ? = sin ? + sin 2?)...
Given vector ? = 2? + 3?, ? = −5? + ? + ?. Find the...
Find the distance traveled with 0 acceleration by (a) indefinite integral, (b) definite integral Please give...
The altitude of a triangle is increasing at a rate of 22 centimeters/minute while the area...
Evaluate ∬ D ( x + y ) d A where D is the region defined...
Find the area of the region under the curve y = e5x from x = 0...
What is the absolute max of f(x) = x^3-3x^2 -9x + 1 over the range of...
use the definition of derivative to find the derivative of f(x) =(x-1)/(x^2 +x)
The force required to maintain the spring at 0.5m is 40 N. And force required to...
SET the following two integrals. Do not calculate. 17a. Find the volume of the solid that...
#6) a) Set up an integral for the volume of the solid S generated by rotating...
Suppose f(x) is a differentiable function such that f(2)=3 and f'(x) is less than or equal...
Consider the following. f(x, y, z) = xe5yz, P(1, 0, 2), u=1/3,-2/3,2/3. (a) Find the gradient...
A population ?(?) can be modeled by the differential equation ??/?? = 0.1? (1 − ?/400)...
Please solve all if possible 1. a) Find an equation of the tangent line to the...
The marketing department of a business has determined that the demand for a product can be...
Use the method of cylindrical shells to find the volume of the solid created by rotating...
Is the function u(x,y)=lnx+y concave or quasiconcave? or both? or neither? Prove your answer.
5. A problem to connect the Riemann sum and the Fundamental Theorem of Calculus: (a) Evaluate...
Use the trapezoidal rule with n = 4 to approximate the integral with a upper bound...
Find the extremum of f(x,y) subject to the given constraint, and state whether it is a...
A plane flies horizontally at an altitude of 6 km and passes directly over a tracking...
Let f(x) = x*(2-x) if x>=0, or x*(x+2) if x<0 i) graph the function from x=-3...
calculatte area of region bounded by y=x^3 y=x^2
cos(arcsec(2x))
The 2x + z = 1 plane when intersecting the paraboloid z = x ^ 2...
Solve a system of linear equations to balance the chemical equation Fe +O2 → Fe2O3
Suppose f is odd and g is even. What is fg? even odd
Consider the function f(x)= x3 x2 − 4 Express the domain of the function in interval...
Find a maximizer and maximum value of: f (x) = x3/5(4 − x).
Compute the line integral of f(x, y, z) = x 2 + y 2 − cos(z)...
For the given cost function C ( x ) = 14400 + 300 x + x^2...
The birth rate of a population is b(t) = 2300e0.024t people per year and the death...
a) Prove: ∇ ∙ (∇f x ∇g) = 0
Find the point of intersection of the following 2 “lines” in the Poincare disk: (Poincare disk...
Determine the equation of a conic that satisfies the given conditions: foci: (-1,2), (7,2) vertices: (-2,2),...
total area bounded by the graphs of y= x^3 -2x & y=x^2 are equal to a....
Find F(x) satisfying: f''(x)= sqrt{x}+x^3+e^x+3 f'(0)=0 f(0)=1
find the derivative 4x^(3) tan(2x) mainly how tan(2x) become sec^2(2x)
Consider the differential equation dy/dx= 2y(x+1) a) sketch a slope field b) Show that any point...
A glass has circular cross sections that taper (linearly) from a radius of 7 cm at...
use a graphing utility to graph the polar equation. inner loop of r=4-6sin find the área...
Finding Upper and Lower Sums for a Region In Exercises 21 and 22, find the upper...
1. Consider the series 1 − 2 /3 + 4 /9 − 8 /27 + ⋯...
express any estrema on p(x)=-2x^3+3x^2+72x in the format of an ordered pair. Specify which type of...
Given the demand function ?(?) = 300 – 0.03?2 and the supply function ?(?) = 0.09?2...
1- Please explain the difference between a Taylor Polynomial of degree 4 and a Taylor Polynomial...
The Washington Monument is the world's tallest obelisk at 555 feet. Suppose a penny is dropped...
The acceleration of a race car during the first 35 seconds of a road test is...
Use logarithmic differentiation to find the derivative of 3x^4x..(no parenthesis around 3x)
Find the volume of the solid formed by rotating the region enclosed by y=e3x+3, y=0, x=0,...
1. t To get full credit for this question make sure you verify that your answer...
1)If f(x)=tanh(2x) then f'(x)= 2) If f(x)=x cosh x+7sin h x then f'(x)= 3) If f(x)=e^cosh(7x)...
Consider the equation x^4 − y^2 = 2xy + 4. Find an equation for the line...
Revisiting Exponential Growth At time t = 0 a population has size 1000. Suppose it grows...
Solve the differential equation: y''= 5x2 - 3x-1/2 where y'(1)= 2 and y(1)= 0
integrate xarctanx from 0 to 1
) Find the maximum value of xy if it is required that 7x + 1y =...
Find the hyperbola equation that satisfies the given conditions : Foci: (1,8) (1,−12); vertices are 4...
Suppose that ? t years from now, one investment plan will be generating profit at the...
Which of the following is a right angle triangle? Show your answers and computation. A.) Triangle...
Consider the function ?(?) = sin(?). Find the Taylor series formula when centered at ? =...
a)Can you evaluate the work done by the field F=Mi+Nj+Pk over a 2d region (such as...
Determine the surface area of a funnel that is generated by revolving the graph of y...
Limits Analytically 3) Calculate the following limit . showing all work for full credit! lim √x+h+4...
Find general solution of the equation: y''' − y'' − y' + y = 2e−x +...
Explain how to use line integral to find the distance travelled by an object along the...
On a highway with a steep incline, the runaway truck ramp is constructed so that a...
Find the eccentricity and the distance from the pole to the directrix of the conic. Then...
y'-4y=e3t y(0)=2
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