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Calculus Questions
Find all the values of x between 0 and 2pi that satisfy the following equations. If...
Please show all work! 6. Sketch graphs that show the following properties: a) The Trapezoid method...
H11-2 The top and bottom margins of a poster are 6 cm and the side margins...
A construction worker pulls a five-meter plank up the side of a building under construction by...
Newton’s law of cooling states that the rate of change of the temperature T of an...
Suppose the centres of two unit spheres are located 1 unit apart. (a) Express the volume...
8. A spring has a natural length of 50cm (0.50m). Applying a force of 1000 N...
Use the given transformation to evaluate the integral. (12x + 12y) dA R , where...
Prove that there is no integer which is a perfect square and is a multiple of...
Find the integral that represents the volume of the solid bounded by the planes y =...
Find the value of c such that the function is continuous on the entire real number...
Evaluate the integral of f(x,y) = x - y/2 when 0 =< y =< 4 and...
Given ??+2?+3?^2=3: (a) Find ?′ by implicit differentiation (leave your answer in terms of ? and...
determine the interval of convergence of the power series ∑ ( 1 to ^ infinity) (n^4...
Use Stoke’s Theorem to evaluate Z C F~ · d~r where F~ = 2y~i+ 6z~j +...
Find the accumulates present value of the following continuous income stream at rate R(t), for the...
Given the function g(x)=4x3−24x2−60xg(x)=4x3-24x2-60x, find the first derivative, g'(x)g′(x). g'(x)=g′(x)= Notice that g'(x)=0g′(x)=0 when x=−1x=-1, that...
Letu=2i−3j+k,v=i+4j−k,andw=j+k. (a) Find u × v and v × u, and show that each of those...
f"(X)=X2, f'(0)=8, f(0)=4 I know that the answer is f(x)=1/2X4+8x+4 but how do I get to...
Let u = ⟨1,3⟩ and v = ⟨4,1⟩. (a) Find an exact expression and a numerical...
Question 1. Find the equation of the tangent line of f(x) =3x2-x+2 at x=2 Question 2....
Find the slope of the secant line between the values x1 and x2 for the function...
3. Find the general solution to the differential equation: (x^2 + 1/( x + y) +...
A dam is inclined at an angle of 30° from the vertical and has the shape...
Calculate the outward flux of the vector field F(x,y) = x[i] + y^2[j] across the square...
find f. f ''(x) = 10 + 6x + 24x2, f(0) = 3, f (1) = 16 f(x)...
Find the exact length of the curve. 36y2 = (x2 − 4)3, 4 ≤ x ≤...
A projectile whose vertical movement is a y(t) - 16t^2 + 224t + 1,920 feet on...
Evaluate lim ?→ ∞ (?^2+?−2) /(?^2−2) lim ?→ ∞ (?+10) √(25?^2+1) lim ?→ −∞ (3?−2) /...
A manufacturer has two factories at which wooden benches can be produced. Let x and y...
determine whether the alternating series ∑ (1 to ^ infinity) (-1)^(n+1) 3^n / (n +1)! is...
Solve the Bernoulli differential equation. The Bernoulli equation is a well-known nonlinear equation of the form...
Let y = y ( t ) be the solution to the initial value problem ...
Periodic doses. Suppose you take 200 mg of an antibiotic every 6 hr. The half-life of...
Use the shell method to find the volume of the solid generated by revolving the region...
Solve the first-order differential equation by any appropriate method. (Enter your solution in the form F(x,...
Define Exact Equations with suitable example? Define Seperable Equaitons with example. What is Integrating Factor, Give...
(x^3)/(sqrt(4-x^2) without using u- substitution
Find the first four nonzero terms in a power series expansion about x=0 for a general...
At what point on the curve x = 3t^2 + 1, y = t^3 − 3...
y=x, y=9x/(1+x^3), Revolve this around the line x = -1 then find volume of the solid
1. Find the equation of the line going through (2, -1) and (3,7) 2. Anvils are...
How can one use a vector valued function tor represent a curve in two dimensions? Explain...
Let F(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 7)j + zk. Find the...
Solve the IVP: (14y^13 + 8x^3 +42xy^5)dy + (12x^3+24x^2y+7y^6)dx = 0, y(2)=1
Approximate the arc length of the curve y=x^-1 over the interval[2,7] using Simpson's rule and 12...
1. (a) Use the graph paper provided to sketch the region bounded by the x-axis and...
Find the directional derivative of f at the given point in the direction indicated by the...
Let R be the region of the plane bounded by y=lnx and the x-axis from x=1...
solve the given initial-value problem y"-100y=15, y(0)=1, y'(0)=0
Use the position function s(t) = −16t2 + v0t + s0 for free-falling objects. A ball...
1) What is a function? Give two examples 2) Solve x2−4=0 factorize 3) Graph following line...
Use the differential equation (1−x)y''−4xy'+5y=cosx(1-x)y′′-4xy′+5y=cosx to answer the following questions: What is the type of the...
1) find the Taylor series expansion of f(x)=ln(x) center at 2 first then find its associated...
Find an equation for the line tangent to the parabola y= 2x^2 -13x +5 which has...
Give an example of a function that increases concave downward on the interval (0, ∞). Justify...
Find the derivative of each function. (a) F1(x) = 3(x4 + 5)5 2 F1'(x) = (b)...
Integrate f(x,y,z) = z over the region enclosed by x^2+y^2=2^2 , z=x^2+y^2 and z=0.
find the Taylors series for f(×) = In(3 +2×) at a=1
Suppose f′(x) = √(x)*sin(x^2) and f(0) = 5. Estimate f(b) for: b = 0 : f(b)...
Solve the problem. On a hot day, a child can sell 31 cups of lemonade if...
Using Leibniz notation (i.e., ??/??, ??/??, etc.), find derivatives for each of the following functions. You...
What is the area between the curves y=−x^2+4 and y=−3?
(10 marks) Solve the second-order linear differential equation y′′ − 2y′ − 3y = −32e−x using...
Find the radius of convergence and the interval of convergence of the power series. (Please check...
Calc 2: Please make sure these are right!! Find the exact length of the curve. x...
Find the number(s) k such that the average value of f(x)=sin3x cos3 x-k on the interval...
Find the solution of the exponential equation (Enter your answers as a comma-separated list.) 3^(2x −...
Find the work it would take to build a limestone pyramid with a square base with...
Find the orthogonal trajectories of the family of curves. ?2 = ky
1. a) an ornamental light bulb is designed by the revolving graph of y=(1/3)x^(1/2) -x^(3/2), 0<x<(1/3)...
(a) Show that the parametric equations x = x1 + (x2 − x1)t, y = y1 +...
[2 marks] Find the derivative of y = √ 4 sin x + 6 at x ...
If z = x2 − xy + 7y2 and (x, y) changes from (3, −1) to...
Let f (x) = −x^4− 4x^3. (i) Find the intervals of increase/decrease of f . (ii)...
Use Lagrange multipliers to find the point on the plane x − 2y + 3z =...
Please let this pass, Just now i wrong uploaded, i want to refund this question ,...
Calculate the line integral of the vector field ?=〈?,?,?2+?2〉F=〈y,x,x2+y2〉 around the boundary curve, the curl of...
Find the direction cosines of v=8i-8j+4k and confirm that they satisfy cos2α+cos2β+cos2γ=1. Then use the direction...
Calculate the volume of the rotational object formed by rotating the given curve with the parametric...
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