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Calculus Questions
use the definition of the derivative to find f′(3) if f(x) = x^2 - 2x
A) You want to cool a substance, which is put into a refrigerator that is at...
Find domain and critical values of A - f(x) = 4x - sqrt(x) B - f(x)...
Consider the following function. (If an answer does not exist, enter DNE.) f(x) = 1 +...
Find the area of the region common to the interiors of the cardioids r =1−sin θ...
Use integration by parts to evaluate the following integrals: (a)? ∫x ln xdx (b)? ∫ x^2...
Determine el dominio de la siguiente función: (5 pts.) ?(?, ?) = √36 − 9? 2...
Estimate the area under the graph of fx=1+x2 from x=-1 to x=3 using 4 rectangles and...
Suppose f(x)=ax^3−x^2+c where a and c are some positive constants. Then f(x) is concave up for...
Oil wells A and B can deliver 25 and 15 units of oil, respectively. Refineries C...
Find the critical values and determine the intervals where ?(?) is decreasing and the intervals where...
Consider the function f(x)=x^7e^4x, −4≤x≤3. The absolute maximum value is and this occurs at x equals...
Find the volume generated by revolving about the x-axis the region bounded by the following graph....
f(x)= (x^2+2x-1)/x^2) Find the a.) x-intercept b.) vertical and horizontal asymptote c.) first and second derivative...
1) Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval....
Find the x-coordinates of all local maxima. g(x)=x^9−3x^7+2 If there are multiple values, give them separated...
A retail store estimates that weekly sales s and weekly advertising costs x (both in dollars)...
Determine the intervals on which the following functions are increasing and decreasing. a) f(x) = 12...
1) Derive the quotient rule ( f g ) ′ = (f ′ ⋅ g −...
Use this equation to find dy/dx. 8 tan−1(x2y) = x + xy2
A particle starts at the origin with initial velocity ⃗v(0) = ⃗i − ⃗j + ⃗k....
Let f(x)=2x^3 - 9x^2 +12x -4 Find the intervals of which f is increasing or decreasing...
Find the absolute maximum and absolute minimum values of f on the interval [0,2] where f(t)=(3y/t^2...
Find the Jacobian of the transformation. x = 5v + 5w2, y = 6w + 6u2, z =...
The flux of F=x^2i+y^2j+z^2k outward across the boundary of the ball (x−2)^2+y^2+(z−3)^2≤9 is:
1) find the absolute extrema of function f(x) = 2 sin x + cos 2x on...
An oil refinery is located 1 km north of the north bank of a straight river...
Evaluate the definite integral. Use a graphing utility to verify your result. (Round your answer to...
Use upper and lower sums (left and right Riemann sums) to approximate the area of the...
For the following function, find where they are increasing/decre asing, concave up/down and any critical numbers...
the height of a triangle increases at a rate of 3 cm / min while the...
the function f given by f(x)=2x^3-3x^2-12x has a relative minimum at x=
Consider the following subset: W =(x, y, z) ∈ R^3; z = 2x - y from...
You are given the following equation. 4x2 + 49y2 = 196 (a) Find dy / dx...
Near the surface of the Earth, the magnitude of the acceleration due to gravity is 32...
Compute the line integral with respect to arc length of the function f(x, y, z) =...
Using the limit process (NOT ANTIDERIVATIVE FORMULAS) evaluate: integral^3 ↓0 of (2x^ 2 − 1)dx
Find the general solution of the given differential equation (x+!) dy/dx + (x+2)y = 2xe^-x y...
True or False? Circle whether the following statements are true or false. Explanations are optional. (a)...
Find the directional derivative Dvf(x,y) where f(x,y) = |x|·|y|.
Let Q1 be a constant so that Q1 = L(20, 12), where z = L(x, y)...
Let Q1 be a constant so that Q1 = L(5, 17), where z = L(x, y)...
An oil refinery is located on the north bank of a straight river that is 2...
We consider the plane region R delimited by the curves y = cos (x) and y...
Find the absolute maximum and minimum values of the following function over the given interval. If...
A bakery works out a demand f(x) for its chocolate chip cookies and finds it to...
(1 point) Find the volume of the solid obtained by rotating the region bounded by the...
i) Approximate the function f(x) = cos x by a Taylor polynomial of degree 3 at...
(b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the...
The annual revenue for Apple in 2008 was $37.5 billion and in 2013 the annual revenue...
Determine the equation of the tangent plane to the surface z = x2y +yz2 +7 at...
A cup of coffee at 90 Celsius is put into a 20 Celsius room, t=0. The...
If a cup of coffee has temperature 100°C in a room where the ambient air temperature...
limx->pi-(3+sinx/1-cosx)
Having trouble understanding. (1 point) Evaluate the triple integral ∭E(xy)dV where E is the solid tetrahedon...
A rectangular storage container with an open top is to have a volume of 10 m3....
1. List the algebraic properties of the cross product in R3. On the same line, write...
Consider the set D which is the triangular region bounded by y=x, x=0, y=4 and the...
Discuss the continuity
Describe the Function y = x^3 - 12x + 7 on [-4,5] completely. Do not use...
Two spacecraft are following paths in space given by r1=〈sin(t),t,t^2〉 and r2=〈cos(t),1−t,t^3〉. If the temperature for...
Use a graph to estimate the coordinates of the rightmost point on the curve x =...
Find the distance traveled by a particle with position (x, y) as t varies in the...
Find the local maximum and minimum values and saddle point(s) of the function. If you have...
Two years ago, doctors found that a benign tumor is growing in a patient’s brain. Though...
A particle is moving along a straight line and has acceleration given by a(t) = 20t^3+12t^2}....
how to sketch the function f(x)= x^2/square root (x+1)
The rate (in mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is...
A tank cylinder hold 54 pi cubic feet of liquid. Minimize or use the least amount...
Find the following for the vectors u= -10+9j+√3k and v= 10i-9j-√3k. a) v*u, |v|, and |u|....
10. Given the price-demand equation: ? = ???? − ?? a) Find the elasticity of demand,...
Find the area of the indicated region. Between y=x and y=x^3 for x in [-1,1]
Find the half-range cosine Fourier series expansion of the function f(x) = x + 3; 0...
Consider an undamped spring with spring constant k = 9N/m and with a mass attached with...
As illustrated in the accompanying figure, a parabolic arch spans a road 40 ft wide. How...
Find the exact extreme values of the function z = f(x, y) = (x-3)^2 + (y-3)^2...
Prove that RL × RL is completely regular. This means RL × RL is an example...
Determine the limit: lim x → ∞ x ^2/x
Find an equation of the sphere determined by the given information. passes through the point (6,...
Find the absolute maximum, and minimum values of the function: f(x, y) = x + y...
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