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Calculus Questions
Find area of the region inside of the rose, r=6sin2θ and inside the circle r =3sqrt(2)
6.(8pts) Find the Average value of ?(?) = 5? sin(?2) on the interval [ 0, √?...
) The velocity function v(t) = −2t + 6, on the interval [1,5] is given for...
draw a contour plot for h(x,y)=2x^2-y-2. show work.
Estimate to the hundredth the area from 0 to 2 under the graph of f(x) =...
Estimate to the hundredth the area from 0 to 2 under the graph of f(x) =...
Q) Find f. f''(x)= −2+36x−12x^2, f(0)=7, f'(0)=12 f(x)= Q) Find f f''(t)=sint+cost, f(0)=2, f'(0)=3 f(t)= Q) Find f f''(x)=20x^3+12x^2+4, f(0)=4, &nbs
A glass with a bowl shaped like a hemisphere of diameter 8 cm contains a marble...
Find the mass of a thin funnel in the shape of a cone z = sqrt...
Using the Taylor series for e^x, sin(x), and cos(x), prove that e^ix = cos(x) + i...
Find the largest open interval where the function is changing as requested. y=(1/x^2) + 7
Saltwater taffy can be sold wholesale for $45 per thousand individual candies. The cost of producing...
A 10 ft. pole weighs 30 lbs. (of force, to be clear). It lies flat on...
A 3m beam has two ends A and B. Its linear density varies. At a point...
Find f. f '''(x) = cos(x), f(0) = 5, f '(0) = 6, f ''(0) = 3
Find the area inside r=3 and outside r=3sin 3 theta
1)Find F f”(x)=-2+36x-12xsquer, f(0)=9, f’(0)=18 f(x)=? 2)Find a function f such that f’(x)=3x cube, and the...
1.Let θ (in radians) be an acute angle in a right triangle and let x and...
Consider the piecewise defined function f(x) = xa− xb if 0<x<1. and f(x) = lnxc if...
For r = f(θ) = sin(θ)−1 (A) Find the area contained within f(θ). (B) Find the...
Use the shortcut rules to mentally calculate the derivative of the given function. HINT [See Examples...
Randy and Rafi’s multimedia company anticipates that there will be a demand for 20,000 copies of...
let g(x) be a continuous function that has exactly one critical point in the interval(-12,-8) find...
Evaluate the surface integral S F · dS for the given vector field F and the...
Assume that the radius r of a sphere is expanding at a rate of 40 cm/min....
State the Fundamental Theorem of Calculus. Why is it such a big deal?
A 200-gallon tank is currently half full of water that contains 30 pounds of salt. A...
Sketch the region enclosed by the given curves. Draw a typical approximating rectangle and label its...
For the given function: f [0; 3]→R is continuous, and all of its values are rational...
Find the derivative of each of the functions below. Please use proper notation for derivatives. Do...
Find the mass of a thin funnel in the shape of a cone z = x2...
Suppose that the average cost, in dollars, of producing a shipment of a certain product is...
A paper cup in the shape of a cone with height 5 cm and radius 3...
Approximate the area under the curve y= x2-2x+4 between x=1 and x=4 by using 6 inscribed...
Find the equation of the tangent line to the graph of the function f(x)=cot2x at the...
Let f(x,y)=2ex+y. Find the second-order Taylor polynomial for f(x,y) at the point (0,0). Group of answer...
a. Approximate the given quantity using Taylor polynomials with n=3. b. Compute the absolute error in...
A ball is thrown into the air by a baby alien on a planet in the...
The tangent plane at (1,1,1) on the surface x2+y2+z2+xy+xz=5 is given by x+ y+ z= (all values...
integral subscript C left parenthesis 12 x plus 6 y right parenthesis d s Where C...
Find the general solution of the given differential equation. y'' + 12y' + 85y = 0...
Find the outward flux of F=32xi+y2j−2yzk across the boundary of D, where D is the region...
Evaluate the surface integral Evaluate the surface integral S F · dS for the given vector...
Gloria would like to construct a box with volume of exactly 55ft3 using only metal and...
1. In planning a restaurant, it is estimated that a profit of $8 per seat will...
Find the equation of the tangent line to x = sint, y = cost when t...
Find f when f''(x)=x+ x^(1/2) and when the following conditions are satisfied f(1)=1 and f'(1)=2
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for...
Use L’Hopital’s Rule to determine if the following sequences converge or diverge. If the sequence converges,...
Find (by hand) all asymptotes and extrema, and sketch a graph: y=x^2/x^2-1 Please show all work...
Suppose we wish to design a closed container that will hold exactly 1 L of gasoline....
the function g(x) is increasing on (-infinity, 2) and (5, infinity). The function is decreasing on...
A lobster tank in a restaurant is 1.25m long by 1m wide by 60cm deep. Taking...
Find the area between the curves y = sinx and y = cosx on the interval...
Calculate the following: absolute maximum, absolute minimum values of f(x, y) = 2x^2y on -> 2x^2+y^2=6
Let R be the region bounded by the curves y = x, y = x+ 2,...
Choose C so that y(t) = −1/(t + C) is a solution to the initial value...
Your monthly cost for your newspaper route is ?(?)=√3?+100 dollars where ? is the number of...
Initial value problem : Differential equations: dx/dt = x + 2y dy/dt = 2x + y...
The number of research articles in a prominent journal written by researchers during 1983–2003 can be...
Determine whether the limit converges or diverges, if it converges, find the limit. an = (1+(4/n))^n
Find a power series expansion for the function f(x)=1/x wither center a=-3. What is its radius...
Problem 1: Which of the following equations represents a plane which is parallel to the plane...
In a town, the population gets infected with a deadly virus that doubles every 3 days....
The total profit(in $) from the sale of x flatscreen television sets is P(x) = 20x...
Inital value Calculus 2 e^(-2x)*y’ = 24x(root(y+1)), y(0) = 0
1) Let div F=2x-5y^(2)+3z. Estimate the flux of F out of a small cube of side...
1. A roast turkey is taken from an oven when its temperature has reached 185°F and...
Find the Taylor series for f(x)= sinx at a=pi/6. (Find up to the fifth degree)
Differentiate but do not simplify: a) x^2(ln(x))^2 b) x^3(arctan(x))^3 c) (ln(x))^2 d) (arctan(x))^2
Suppose a recent college graduate's first job allows her to deposit $200 at the end of...
A bakery works out a demand function for its chocolate chip cookies and finds it to...
A personal account earmarked as a retirement supplement contains $242,400. Suppose $200,000 is used to establish...
Find the Maclaurin series for ?(?) using the definition of a Maclaurin series and find at...
Find the equation of the tangent plane to the surface ?=7?^2+9?^2+2?? at the point (1,−1,14). ?=
Evaluate the integral: ∫27√x^2−9 / x^4 dx (A) Which trig substitution is correct for this integral?...
Evaluate the integral: ∫8x^2 / √9−x^2 dx (A) Which trig substitution is correct for this integral?...
given function f(x)=-x^3+5x^2-3x+2 A) Determine the intervals where F(x) Is increasing and decreasing b) use your...
Please solve this using the superposition approach y''+4y'+5y=e^(-2x)cos x
Species A doubles every 1 hours and initially there are 5 grams. Species B doubles every...
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