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Calculus Questions
Find the indicated maximum or minimum value of f subject to the given constraint. Minimum :...
Find the intervals on which f(x) = x^4 + 2x^3 − 36x^2 + 9x − 47...
Discuss the derivative and integral in terms of units. For each, provide a real-world example to...
find the accumulated present value of the following continuous income stream at rate R(t), for the...
Given f(x)=2cos(3x), write the equation of the line tangent to y=f(x) when.x=\frac{\pi}{4}
3. Integrate using partial fractions (Lesson 8) integral 2 to 1 (x^4 + 1)/x(x2 + 1)^2...
Verify that f(x)= ln(x) satisfies the hypothesis of the Mean Value Theorem on the interval [1,6]...
The temperature at a point (x, y, z) is given by T(x, y, z) = 400e−x2...
Let f be a function differentiable on R (all real numbers). Let y1 and y2 be...
Find all local extrema for f(x, y) = 2y3 + 18x2 − 36xy. (If an answer...
integral from -6 to 6 of sqrt(36-x^2)^3 dx
Evaluate the following integral. ∫ (x3 − 3x2)( 1 x − 3) dx (A) − 3...
Using the Taylor Remainder Theorem, what is the upper bound on | f (x) − T3(x)|,...
Consider the function x3−6x2+9x+3.8. Find the global maximum of the function on the interval [2,3.3]. Round...
Show complete and neat solution. Find the distance between the skew lines ?1:? = 1 +...
In this question, you will work step-by-step through an optimization problem. A craftswoman wants to make...
The exponential decay function for 100 mg of the radioactive isotope californium-253 is given by the...
A thermometer is removed from a room where the temperature is 70° F and is taken...
Show complete solution. 1. Find two unit vectors that are parallel to the ?? −plane and...
Use Lagrange multipliers to find the maximum value of the function f(x,y) = xy given the...
3. The velocity function of a particle is moving on a coordinate line is given by...
Suppose you invest $10,000 in an account which pays 4% interest per year compounded quarterly. Use...
Find the derivative r '(t) of the vector function r(t). <t cos 3t , t2, t...
1/4y''+4y=tan4t-1/2e^(2t) Find a general solution to the differential equation.
a piece of pizza in the shape of a sector with angle, theta, and radius, r,...
(Optimization Problem) You need to fence in a rectangular area for a garden outside of your...
Use cylindrical coordinates. Where E lies below the cone ϕ = π/4 and above the sphere...
Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as...
Find 6 different iterated triple integrals for the volume of the tetrahedron cut from the first...
Find the volume of the solid generated by revolving the region bounded by y = 1sqrtx...
Question 1 [20 marks in total] For each part, determine the domain of each expression (the...
(a) Approximate the area of the region beneath the graph of f(x) = e−x2, from x...
Consider the function f(x) = x^3 − 2x^2 − 4x + 7 on the interval [−1,...
(1 point) The function f(x)=3x+5x^−1 has one local minimum and one local maximum. This function has...
A closed rectangular box is to contain 12 ft^3 . The top and bottom cost $3...
Evaluate the given integral by making an appropriate change of variables. 7 x − 8y 4x...
The rate of growth of a certain cell culture is proportional to its size. In 8...
The demand function for x items of a certain product is given by the following function...
Use Linear Approximation to estimate Δ?=?(13.02)−?(13) for ?(?)=?^4. (Use decimal notation. Give your answer to two...
Find the linearization of ?=(1+5?)^(−1/2) at ?=3. (Use symbolic notation and fractions where needed.)
Fruit flies are placed in a half-pint milk bottle with a banana (for food) and yeast...
Fruit flies are placed in a half-pint milk bottle with a banana (for food) and yeast...
Problem 3. Consider the function f(x) = -3r2 + 3 and the rectangle given by the...
The monthly demand function for x units of a product sold by a monopoly is p...
11. At what rate of interest compounded continuously, will an investment triple in 9 years? 12....
Solve the initial-value problem. (x2 + 1) dy dx + 3x(y − 1) = 0, y(0)...
find number of units x, that produce the maximum profit P, if C(x)=50+68x and p=80-2x
for w=f(x,y,z)=2x^4y^2-6xz^3 use the tangent plane to estimate f(-2.03,1.04,1.02)
f(x, y) = ln x + x2 + y2 ; fx(5, −3)
Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service...
Let S be the region bounded by ? = ?^?^2, ? = 0, ? = 1,...
The demand function for a Christmas music CD is given by q=0.25(225−p^2) where q (measured in...
Evaluate the surface integral ∬ 4? ? ??, where ? is the portion of the sphere...
In what direction does ?(?,?)= ln(9?^2+6?^2) increase most rapidly at (2,5)? (Enter a unit vector.)
Integrate: ∫ 2 x √ x + 3 d x
Evaluate the improper integral or state that it is divergent. upper ∞ ∫ bottom 1 9/ (1+x^2)...
The Island of Youth’s Gross Domestic Product (GDP) (in millions of dollars) is described by the...
Suppose ?(?) is continuous on [4,6] and −4 ≤ ?′(?) ≤ 2 for all ? in...
1) Keep the proportionality and the constant of proportionality in mind. The rate of growth of...
Find the critical numbers of the function. 18 cos(θ) + 9 sin2(θ)
A radioactive material disintegrates at a rate proportional to the amount currently present. If Q(t) is...
1. Let ?(?)=−?4−4?3+8?−1. Find the open intervals on which ? is concave up (down). Then determine...
What is the mass of a metal rod following y=sqrt(x) on x∈[1,4] with its density given...
1. (Continued) Consider the function (e) (f) f (x) = x3 − 7 x + 5....
The region bounded by y=2^x and y=4x-4 is rotated about the line y=3. Find the volume...
A baseball diamond is a square with sides of length 90 ft. A batter hits the...
Show that f(x)=x4+4x-2 has exactly one real root in the interval [0, ∞)
Show that the equation x+sin(x/3)−8=0 has exactly one real root. Justify your answer.
What is the rectangle of maximal area constructed with its base on the diameter of a...
i. A trough is 12 ft long and its ends have the shape of isosceles triangles...
the function x^8 + y^8 has a critical point at (0,0). What sort of critical point...
Find the area between f(x)=x2-x and the x-axis between x=0 and x=2. Note that f(x)>0 between...
Find the area of the indicated region. We suggest you graph the curves to check whether...
Gravel is being dumped from a conveyor belt at a rate of 25 ft3/min, and its...
17. A ship's course is set at a heading of 143 at 18 knots. A 10-knot...
Let f(x) = 4x^5 − 5x^4 + 9. (a) Find each critical number for f. (b)...
answer the following questions about the function whose derivative id f'(x)=(x^2(x-4))/(x+6) , x does not equal...
Suppose you know that f′(x) = x sin(2x) − sin(2x). Find the x-coordinates of all local...
Find the interval of convergence for the power series ∑?=0∞ 8?(?−5)3?+1 Give your answer using interval...
Find an equation of the tangent line to the graph of 2x+5/(1-2x)^3 at the point (-1,1)
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