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Calculus Questions
Evaluate the integral. 7 t^3i+t(t-6)^1/2j+tsin(pit)k dt 6
solve the initial value problem y' y" - t = 0 y(1) = 2 y'(1) =1
find all the second partial derivatives of f(x,y)= x^2y^2+3sinxtany
A ball is launched straight up in the air from a height of 66 feet. Its...
In 2003, there were 15,600 students at college A, with a projected enrollment increase of 1000...
1. Let ?(?)=8(sin(?))? find f′(2). 2. Let ?(?)=3?sin−1(?) find f′(x) and f'(0.6).
In a certain culture where the rate of growth is proportional to the number present, the...
Figure out the point of intersection of the three planes using the Gauss-Jordan elimination method: 2x...
Using the method of Lagrange Multipliers, find the point on the plane x+y−z=1 that is closest...
1- Differentiate the function g(x) = 7/8x^2 - 7 x + 14 g'(x) = 2- Differentiate...
Determine the volume of the tetrahedron cut from the first octant by the plane 6x +...
1. What is a relative min extrema (x,y) for f(x) in f(x) = 2x3+3x2-12x+5 ? 2....
Given the function M(t) = 2t^3 – 3t^2 – 36t, find the critical values and determine,...
A company makes two types of magazine racks, metal and plastic. The metal magazine racks sell...
Find the volume V obtained by rotating the region bounded by the given curves about the...
1. You've had birthday and forgot to bring breakfast with you at work, so your colleagues...
Find the critical point of the function f(x,y)=x2+y2+xy+12x c=________ Use the Second Derivative Test to determine...
Find the positive value of x that satisfies x=1.3cos(x). Give the answer to six places of...
USING DIFFERENTIAL EQUATIONS To supply an isolated person on an island, they throw a bag of...
1. a) Get the arc length of the curve. r(t)= (cos(t) + tsin(t), sin(t) - tcos(t),...
1) If 67+3?(?)+4?^2(?(?))^3=0 and ?(−4)=−1, find ?′(−4). f'(-4)= 2) Find an equation of the tangent...
1. Find the derivative of f(x)= √4-sin(x)/3-cos(x) 2. Find the derivative of 1/(x^2-sec(8x^2-8))^2
According to the National Health Survey, the heights of adult males in the United States are...
Find a co-terminal angle between 0 degrees and 360 degrees for the angle given: 1525 degrees
2.the graph of x^2 -xy+y^2=6 is a tilted ellipse. Find the coordinated on which the tangent...
For a limited time interval, the current through a 9.71 microhenries (or, equivalently, 9.71×10^-6 henries) inductor...
A particle moves according to a law of motion s = f(t), t ≥ 0, where...
Find the general solution for the given differential equation x2y′′−5xy′+13y=2x3x2y′′−5xy′+13y=2x3 NOTE: Write your answer clearly in...
The demand for cat food is given by D(x)=110e^−0.02x where x is the number of units...
The base of a solid is the region bounded by y = 9 and y =...
made a mistake cancel question
Find the area of the "triangular" region in the first quadrant that is bounded above by...
A small company of science writers found that its rate of profit (in thousands of dollars)...
A box with an open top is to be constructed from a square piece of cardboard,...
1. A trail of ants on a silo is described by the helix ?: ?⃗(?) =...
Choose one of the following statements to discuss the validity of the statement . if the...
If a cannonball is shot directly upward with a velocity of 208 feet per second, its...
According to Zipf's Law, the number of cities N with a population greater than S is...
Anthony works at a plant that makes a solution for brining hotdogs. A tank with a...
Suppose you want to build a hollow rectangular box with volume 2000 cm^3. If the material...
(1 point) Suppose P=f(t)P=f(t) is the population (in thousands) of town tt years after 1990, and...
The demand for q units of a product depends on the price p (in dollars) according...
7. What is the idea of the Runge-Kutta method?
Sketch the regions enclosed by the curves x= sin 5y and x=10y/pi, and compute its area...
1) Let f(x)=−x^3−12x^2−45x+2 a) Find the open interval(s) where the following function is concave upward or...
List any extrema, inflection point, intervals of concavity, and then sketch the graph. ?(?)=?3 −?2 −?+1
Let y = x 2 + 3 be a curve in the plane. (a) Give a...
Use the following information to graph the function f over the closed interval [-2,5]. I.) The...
Find the general solution: 2x''+ 3t x'+x= 0
1. y=∫upper bound is sqrt(x) lower bound is 1, cos(2t)/t^9 dt using the appropriate form of...
The sales of a new high-tech item (in thousands) are given by S(t)=105-90e^ (-0.4 t) where...
Solve the initial value problem below using the method of Laplace transforms. y"+11y'+30y=280e^2t, y(0)=1, y'(0)=32
Find the derivative of the function at P0 in the direction of u. f(x, y) =...
find the taylor series of f(x)=x^2 * arctan(x^2) at b = 0
find the volume of the solid generated by revolving the region about the axis. use the...
1). Find the consumer and producer surpluses by using the demand and supply functions, where p...
i). Given the series: A. Find the radius and the interval of convergence. B. Determine the...
Glorious Gadgets is a retailer of astronomy equipment. They purchase equipment from a supplier and then...
Let f(x) = 1 + x − x2 +ex-1. (a) Find the second Taylor polynomial T2(x)...
Consider the following functions. f1(x) = x, f2(x) = x2, f3(x) = 6x − 4x2 g(x) = c1f1(x)...
For this problem, consider the function f(x) = ln(1 + x). (a) Write the Taylor series...
Production The production function for a company is given by f(x, y) = 100x0.6y0.4 where x...
Find the 5th Taylor polynomial of f(x) = 1 + x + 2x^5 +sin(x^2) based at b...
Give an example of a rate of change that is used in some real world situation...
Differential Equations ?'''' − ?''' − ?'′ − ? ′ − 2? = 8?^5 Find ??...
Consider the function on the interval (0, 2π). f(x) = sin(x) cos(x) + 2 (a) Find...
find the derivative of the function and f'(x) at x=4 f(x)= (sqrt(x)+5x) ((x^3/2)-x)
find the double integral that represents the volume of the solid entrapped by the planes y=0,...
For the function f(x)=x^5+5x^4-4. Write "none" if there isn't an answer. (a) find all local extrema...
Find the center of mass of a thin plate covering the region bounded below by the...
Find the center of mass of a thin plate of constant density δ covering the given...
A container of hot liquid is placed in a freezer that is kept at a constant...
Find the length of the arc of y=x^2 from (1,1) to (2,4).
Find the area of the shaded region. y=x^2-4x+3 and y=x-1
17) A ball is thrown vertically upward from ground level with an initial velocity of 96...
find the taylor series of ln 2x centered at x=2
2. Find the absolute maximum and minimum values of the function f(x, y) = 2x^3 +...
A) Use the Comparison Test to determine whether integral from 2 to infinity x/ sqrt(x^3 -1)dx...
When the brakes are applied, a car decelerates at 0.7 meters per second per second. Use...
Prove the following (4 sin(θ) cos(θ))(1 − 2 sin2 (θ)) = sin(4θ) cos(2θ) /1 + sin(2θ)...
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